Embed Size (px)
Citation preview
PROCEEDING BOOK
5th International Conference on Advances in Statistics
2
APRIL 22-24 2019
Athens/Greece
http://www.icasconference.com/
3
ICAS’2019
5th International Conference on Advances in Statistics
Athens/Greece
Published by the ICAS Secretariat
Editor:
Prof. Dr. Fatma NOYAN TEKELİ
ICAS Secretariat Büyükdere Cad. Ecza sok. Pol Center 4/1 Levent-İstanbul
E-mail: [email protected] http://www.icasconference.com
Conference organised in collaboration with Smolny Institute of the
Russian Academy of Education
Copyright @ 2019 ICAS and Authors
All Rights Reserved No part of the material protected by this copyright may be reproduced or utilized in any form or by any means electronic or mechanical, including
photocopying , recording or by any storage or retrieval system, without written permission from the copyrights owners.
4
SCIENTIFIC COMMITTEE
Prof. Dr. Aydın ERAR Mimar Sinan Fine Arts University – Turkey
Prof. Dr. Ayman BAKLEEZI Qatar University – Qatar
Prof. Dr. Barry C. ARNOLD University of California, Riverside – USA
Prof. Dr. İ. Esen YILDIRIM Marmara University – Turkey
Prof. Dr. Fatma NOYAN TEKELI Yıldız Technical University – Turkey
Prof. Dr. Gülhayat GÖLBAŞI ŞİMŞEK Yıldız Technical University – Turkey
Prof. Dr. Gülay BAŞARIR Mimar Sinan Fine Arts University – Turkey
Prof. Dr. Hamparsum BOZDOGAN The University of Tennessee – USA
Prof. Dr. Hamzeh TORABI Yazd University – IRAN
Prof. Dr. İsmihan BAYRAMOGLU (BAIRAMOV) Izmir University of Economics – Turkey
Prof. Dr. Jorge NAVARRO Facultad de Matematicas, Universidad de Murcia – Spain
Prof. Dr. Jose Maria SARABIA University of Cantabria – Spain
Prof. Dr. Leda MINKOVA
Department of Probability, Operations Research and Statistics University of Sofia “St. Kliment Ohridski
Prof. Dr. Müjgan TEZ Marmara University – Turkey
Prof. Dr. Narayanaswamy BALAKRISHNAN Keynote Speaker / McMaster University – Canada
5
Prof. Dr. Nikolai KOLEV Department of Statistics, University of Sao Paulo
Prof. Dr. Şahamet BÜLBÜL Marmara University – Turkey
Prof Dr Sarjinder SINGH Texas A&M University-Kingsville – USA
Prof Dr Stelios PSARAKIS Athens University of Economics & Finance – GREECE
Assoc. Prof. Dr. Barıs ASIKGIL Mimar Sinan Fine Arts University – Turkey
Assoc. Prof. Dr. Esra AKDENİZ Marmara University – Turkey
6
ORGANIZATION COMMITTEE
Prof. Dr. Gülhayat GÖLBAŞI ŞİMŞEK
Yıldız Technical University – Turkey
Conference Chair
Prof. Dr. Fatma NOYAN TEKELİ Yıldız Technical University – Turkey
Prof. Dr. Hamparsum BOZDOGAN The University of Tennessee – USA
Prof. Dr. İsmihan BAYRAMOGLU (BAIRAMOV) Izmir University of Economics – Turkey
Assoc Prof. Dr. Barış ASIKGİL Mimar Sinan Fine Arts University – Turkey
Assoc. Prof. Dr. Gülder KEMALBAY Yıldız Technical University – Turkey
Instructor PhD Ozlem BERAK KORKMAZOĞLU Yıldız Technical University – Turkey
7
Dear Colleagues,
On behalf of the Organizing Committee, I am pleased to invite you to participate in 5th
INTERNATIONAL CONFERENCE ON ADVANCES IN STATISTICS which will be
held in Athens, Greece dates between 22-24 April 2019 .
We cordially invite prospective authors to submit their original papers to ICAS-2019, Athens.
. Applied Statistics
· Banking, Finance, Insurance, Actuarial
Sciences and Risk Management
· Bayesian Statistics
· Big Data Analytics
· Bioinformatics
· Biostatistics
· Clinical Trials
· Combinatorics
· Computational Statistics
· Data Analysis and Modeling
· Data Envelopment Analysis
· Data Management and Decision Support
Systems
· Data Mining
· Demography
· Experimental Design
· Energy and Statistics
· Entrepreneurship
· Entropy
· Fuzzy Theory and Statistical Applications
· Genetic Algorithms
· Mathematical Foundations of Statistics
· Mathematical Statistics
· Multivariate Statistics
· Neural Networks and Statistics
· Non-parametric Statistics
. Operations Research
· Optimization Methods in Statistics
· Order Statistics
· Panel Data Modelling and Analysis
· Performance Analysis in Administrative
Process
· Philosophy of Statistics
· Public Opinion and Market Research
· Quality Control
· Regression Models
· Reliability Theory
· Sampling Theory
· Simulation Techniques
· Spatial Analysis
· Statistical Software
· Statistical Training
· Statistics Education
· Statistics in Social Sciences
· Stochastic Processes
· Supply Chain
· Survey Research Methodology
· Survival Analysis
· Time Series
· Water and Statistics
· Other Statistical Methods
Selected papers will be published in Communications in Statistics-Theory and Methods,
indexed by SCI-Expanded.
We hope that the conference will provide opportunities for participants to exchange and
discuss new ideas and establish research relations for future scientific collaborations.
In addition to scientific program there will be also social activities including sightseeing
which we hope will leave a pleasant trace on your memory.
Conference Website : http://icasconference.com
E Mail: [email protected]
On behalf of Organizing Committee:
Conference Chair
Prof. Dr. Gülhayat GÖLBAŞI ŞİMŞEK, Yıldız Technical University
8
22 APRIL 2019 MONDAY
08:30-17:00 : REGISTRATION
MAIN HALL : OPENING CEREMONY
09:40 – 10:00
Welcome Speech : Prof. Dr. Gülhayat Gölbaşı Şimşek / Yıldız Technical
University
Conference Chair
HALL 1/ KEYNOTE SPEECH A
10:00 –
10:40
Keynote Speech: Prof. Dr. Ismihan BAYRAMOGLU
Speech Title: On Some New Results on Order Statistics and
Applications in Reliability Analysis
10:40 – 11:00 C O F F E E / T E A B R E AK
HALL 1 / SESSION A
SESSION
CHAIR
Prof. Dr. Ismihan BAYRAMOGLU
TIME PAPER TITLE PRESENTER / CO
AUTHOR
11:00 – 11:20 QUANTILE TRANSFORMATION
BASED BAYES CLASSIFICATION AT
GENE EXPRESSION LEVEL
Necla KOCHAN, Yazgı G.
TÜTÜNCÜ, Göknur GINER,
Luke GANDOLFO
11:20 – 11:40 A NOTE ON BIVARIATE RECORDS Gülder KEMALBAY
11:40 – 12:00 SMOOTH NONPARAMETRIC
REGRESSION UNDER SHAPE
RESTRICTIONS
Hongbin GUO, Yong Wang
12:00 – 12:20 COHERENT SYSTEMS UNDER
MARSHALL-OLKIN RUN SHOCK
MODEL
Murat OZKUT
12:20 – 13:20 LUNCH
HALL 1 / SESSION B
SESSION
CHAIR
Prof. Dr. Pınar AKKOYUNLU
TIME PAPER TITLE PRESENTER / CO
AUTHOR
13:20 – 13:40 A SEARCH FOR A BETTER HEDONIC Sinem Guler KANGALLI
9
OFFICE RENT MODEL FOR ISTANBUL:
INSIGHTS FROM PARAMETRIC VS.
SEMIPARAMETRIC APPROACHES
UYAR
13:40 – 14:00 CONSTRUCTING LOCATION-SPECIFIC
PRICE INDEXES FROM SCANNER
DATA
Lun LI
14:00 – 14:20 PARAMETER ESTIMATION WITH
JACKKNIFE AND WEIGHTED MEDIAN
IN
NON-PARAMETRIC REGRESSION
ANALYSIS
Necati Alp ERILLI
14:20 – 14:40 FORECASTING FINANCIAL TIME-
SERIES USING DATA MINING MODELS:
A SIMULATION STUDY
Imad Bou-HAMAD,
Ibrahim Jamali
14:40 – 15:00 THE IMPACT OF TWEET SENTIMENTS
ON TECH STOCK RETURNS: AN
APPLICATION OF ASYMMETRIC
GRANGER CAUSALITY
Umut UYAR, Melike
YAVUZ
15:00 – 15:20 C O F F E E / T E A B R E AK
HALL 1 / SESSION C
SESSION
CHAIR Phd. Huan Yang
TIME PAPER TITLE PRESENTER / CO
AUTHOR
15:20 – 15:40 CROSS-BORDER M&A AND THE
PERFORMANCE OF ACQUIRER:
IN THE PRESENCE OF THE ORIGIN
EFFECT AND HETEROGENEOUS
TREATMENT UNDER MULTI-REGION
CONTEXT
Huan YANG
15:40 – 16:00 AN EMPIRICAL ANALYSIS OF
PRODUCTIVITY AND INDUSTRIAL
CONCENTRATION IN TURKISH
MANUFACTURİNG INDUSTRIES
Aytekin GUVEN, Cevsen
CIFTCI
16:00 – 16:20 MULTIVARIATE ANALYSIS
BETWEEN WEB-BASED HOMEWORK
AND ACHIEVEMENT AT
STATISTICAL COURSE
MELTEM UCAL
16:20 – 16:40 SME FINANCE: IMPACT ON GROWTH Edna Stan-MADUKA,
10
AND DEVELOPMENT Sonny Nwankwo
23 APRIL 2019 TUESDAY
08:30-17:00 : REGISTRATION
HALL 1/ KEYNOTE SPEECH B
09:40 – 10:40 Keynote Speech: Prof. Dr. MIKE TSIONAS
Speech Title: Bayesian analysis of multi-objective portfolio problems
10:40 – 11:00 C O F F E E / T E A B R E AK
HALL 1 / SESSION D
SESSION
CHAIR
Prof. Dr. Pınar AKKOYUNLU
TIME PAPER TITLE PRESENTER / CO
AUTHOR
11:20 – 11:40 THE NEW GENERATION AND THE
WORLD OF WORK
Regina Zsuzsánna
REICHER
11:40 – 12:00 NOTION OF SUBJECTIVE WELLBEING
IN BULGARIA: MICROECONOMETRIC
ANALYSIS USING CATEGORICAL
RESPONSE
MODELS BASED ON ESS DATA
VENELİN BOSHNAKOV
12:00 – 12:20 THE DYNAMICS OF INCREASING LAND
PRICES IN THE PERI-URBAN LAND
MARKETS OF DEVELOPING
COUNTRIES : A CASE STUDY OF
BENGALURU METROPOLITAN CITY,
INDIA
Amrutha Mary VARKEY
12:20 – 12:40 FORECASTING REGIONAL INFLATION
AND UNEMPLOYMENT: THE ROLE OF
SPATIAL SPILLOVERS
Casto Martin Montero
KUSCEVIC
12:40 – 13:20 LUNCH
HALL 1 / SESSION E
SESSION
CHAIR
Prof. Dr. Gulhayat GOLBASI SIMSEK
TIME PAPER TITLE PRESENTER / CO
AUTHOR
13:20 – 13:40 MULTI-CRITERIA DECISION MAKING
METHODS BASED ON
Nimet Yapıcı PEHLİVAN,
11
INTUITIONISTIC FUZZY SETS Yasemin GÜNTER
13:40 – 14:00 DATA CLEANING: BIG DATA
ANALYTICS FOR SMART CITIES
Carla Susete FRANCISCO,
Ana Raquel CASTANHO,
Tiago FONSECA
14:00 – 14:20 PHASE I DISTRIBUTION-FREE
CONTROL CHARTING METHODS
BASED ON CHANGE-POINT
ANALYSIS FOR OUTBREAK
DETECTION
Christina PARPOULA,
Alex KARAGRIGORIOU
14:20 – 14:40 MODELLING OF MULTI-STATE
SYSTEMS VIA A MARKOV
SWITCHING APPROACH
Emmanouil-Nektarios
KALLIGERIS, Alex
KARAGRIGORIOU,
Christina PARPOULA
14:40 – 15:00 SURVEYING THE RATE OF RETURN
OF ASSETS OF TURKISH BANKS WITH
INDEPENDENT COMPONENT
ANALYSIS
GÜLHAYAT GÖLBAŞI
ŞİMŞEK Zehra CİVAN,
UTKU KUBİLAY ÇINAR
15:00 – 15:20 INFERENCES OF FIRTH LR, FLIC AND
FLAC IN TERMS OF BIAS IN RARE
EVENT CASE
Ezgi NAZMAN, Hülya
OLMUŞ, Semra ERBAŞ
POSTER PRESENTATION
15:20 –
15:40
EXPLORING STATISTICAL MODELS: HUMAN
RESPONSE TIME DISTRIBUTIONS ON
PSYCHOLOGICAL EXPERIMENTS THEORY
Carla Susete G.
FRANCISCO, Filipa
RIBEIRO, José António
S. MACIAS,
APPLICATION OF TIME
SERIES MODELING FOR TOURISM : A CASE
OF TURKEY
Özlem BERAK
KORKMAZOĞLU
15:40 – 16:00 C O F F E E / T E A B R E AK
HALL 1 / SESSION F
SESSION
CHAIR
Prof. Dr. Alex KARAGRIGORIOU
TIME PAPER TITLE PRESENTER / CO
AUTHOR
16:00 – 16:20 MODELLING OF FACTORS
INFLUENCING THE CITATION COUNTS
IN STATISTICS
Olcay ALPAY, Nazan
DANACIOĞLU, Emel
ÇANKAYA
16:20 – 16:40 THE PROBABILITY OF GIVING BIRTH
TO A GIRL BETWEEN PROBABILISTIC
Samah Gamal Ahmed
ELBEHARY
12
AND DETERMINISTIC REASONING “A
CASE STUDY OF STUDENTS
TEACHERS IN EGYPT”
16:40 – 17:00 A CREDIT DEFAULT SWAP
APPLICATION BY USING QUANTILE
REGRESSION TECHNIQUE
Yuksel Akay UNVAN,
Hüseyin Tatlıdil
17:00 – 17:20 MARKOV-MODULATED LINEAR
REGRESSION AS ALTERNATING ONE
Nadezda SPIRIDOVSKA,
Alexander ANDRONOV
17:20 – 17:40 APPLICATION OF MACHINE
LEARNING FOR THE VALIDATION OF
BEHAVIOURS OF SPRING CALVING
DAIRY COWS AS INDICATIVE OF
INSUFFICIENT GRASS ALLOCATION
Abu SHAFIULLAH,
Jessica WERNER, Christina
UMSTATTER, Emer
KENNEDY, Lorenzo LESO,
Bernadette O‘BRIEN
17:40 – 18:00 BETA-TRUNCATED-GEOMETRIC
DISTRIBUTION WITH APPLICATION IN
MODELING COUNT DATA WITH
APPLICATIONS
Zainab All balushi
24 APRIL 2019 WEDNESDAY
08:30-17:00 : REGISTRATION
HALL 1 / SESSION G
SESSION
CHAIR
Prof. Dr. FATMA NOYAN TEKELİ
TIME PAPER TITLE PRESENTER / CO
AUTHOR
09:40 – 10:00 EFFECT OF JOB STRESS ON JOB
SATISFACTION IN WHITE COLLAR-
WORKERS: AN APPLICATION OF
STRUCTURAL EQUATION MODELLING
Batuhan ÖZKAN , Fatma
NOYAN TEKELI
10:00 – 10:20 TURKEY LABOR MARKET FOR THE
EFFECT OF REGULATION OF THE
STATE UNEMPLOYMENT: 1988-2018
PERIODS OF INTERVENTION ANALYSIS
Zeynep KARACOR ,
Burcu GUVENEK, Asiye
KAYHAN
10:20 – 10:40 ANALYSIS OF AIR QUALITY WITH TIME
SERIES ANALYSIS AND ARTIFICIAL
NEURAL NETWORKS
Fadime AKSOY, Derya
TOPDAG
11:00 – 11:30 CLOSING CEREMONY
13
5th
International Conference on Advances in Statistics
EXPLORING STATISTICAL MODELS: HUMAN RESPONSE TIME DISTRIBUTIONS
ON PSYCHOLOGICAL EXPERIMENTS THEORY
Carla Susete G. FRANCISCO, Filipa RIBEIRO, José António S. MACIAS ........................... 14
EFFECT OF JOB STRESS ON JOB SATISFACTION IN WHITE COLLAR-WORKERS
AN APPLICATION OF STRUCTURAL EQUATION MODELLING
Batuhan ÖZKAN , Fatma NOYAN TEKELİ ......................................................................... 21
A CREDIT DEFAULT SWAP APPLICATION BY USING QUANTILE REGRESSION
TECHNIQUE
Yüksel Akay Ünvan, Hüseyin Tatlıdil .................................................................................... 36
14
Exploring statistical models: Human Response time distributions
on psychological experiments theory
Carla Susete G. FRANCISCO1, Filipa RIBEIRO2, José António S. MACIAS3
1Catholic University of Portugal, Lisbon, Portugal; [email protected] 2Catholic University of Portugal, Lisbon, Portugal;
[email protected] 3University of Corunna, Corunna, Spain; [email protected]
Abstract Reaction Time (T), or latency, is the interval between the presentation of a stimulus and the response to it. With
modern computer-based equipment it is possible to obtain very large data sets of individual's reaction time (T), with
latency measurements, and determinate the variability of the responses. Theoretical and practical works have shown that latency is in the order of 200 ms,. The result is always a skewed distribution, with a longer tail to the right. The distribution does not fit, particularly well, with any one of the more standard mathematical distributions (Gaussian, Poisson, Gamma, etc.). Observed variability in reaction time might well be due to a variability in the rate of the underlying process. Looking at the reciprocal of reaction time (1/T) promptness, we can obtain a distribution of the promptness or reciprocal reaction time for studying the correspondence with any of the most common distributions such as Gaussian, Poisson, etc. The distribution of the reciprocal of reaction time is not only symmetrical but actually looks as though it might be Gaussian. If it were, that would not only make it easier for mathematical analysis but would also
suggest that we had reached a genuinely fundamental phenomenon. We use a graphical procedure to convert our histogram into a cumulative histogram. For it, we are using a special distorted scale, this time on the vertical, probability axis namely a reciprobit plot. In this case, if the distribution is indeed Gaussian, we should get a straight line. Experimental data can summarize what this approach provides as a mean for characterizing reaction time behavior with a very small number of parameters. It is enough to specify the median and intercept of the main distribution. Moreover, the obtained results allow us to suppose that the delay in the response of the human intermittent control can be determined by cumulative actions of two distinct, automatic and intentional mechanisms, giving it complex non-linear properties.
Key Words: Reaction Time, Fieller Distribution, LATER model, ELATER model, Recinormal Distribution
1. Introduction Reaction time (RT), or latency, is the interval between presenting a stimulus and making a response to
it. One of the most study objects in reaction time is the saccade. That is the eye movement we make to
look at a target in our field of view; we make two or three saccades every second of our lives. Latency in
saccades is in the order of 200 ms., see Robinson (1964). With modern equipment based on computational
systems, it is possible to obtain very large datasets of saccadic latency measurements and to determine the
form of their variability. The result is always a skewed distribution, with a longer tail to the right. This
distribution does not fit particularly well in any of the most common standard mathematical distributions (Gaussian, Poisson, Gamma, etc.). We define the reciprocal of reaction time (1 / T) as promptness. The
distribution of the reciprocal of reaction is not only symmetrical, but actually looks as though it might be
Gaussian. If it were, that would not only make for easier mathematical analysis, but would also suggest
that we had reached a genuinely fundamental phenomenon. A graphical procedure is designed to convert
our histogram into a cumulative histogram. For it, we are using a specially-distorted scale, this time on the
vertical, probability axis (a reciprobit plot). In this case, if the distribution is indeed Gaussian, we should
get a straight line. This approach provides means of characterizing the behavior of the reaction time using
experimental data that is summarized through a very small number of parameters, since it is sufficient to
specify a median and the intercept of the main distribution [1].
2. Models for analyzing the Reaction Time. Mathematical models try to analyze the treatment of reaction time (RT) of individuals in front of an
external stimulus. Under identical conditions, long-term monitoring of the individual RT shows
significant variations in time. This variability is, a priori, modeling as a distribution function close to
Normal distribution function. But empirical results show a tendency to presence of levels of skewness
(positive asymmetry), and some type of distributions would be better options.
15
The traditional approach to the reaction time model considers some type of decision signal, starting at
an initial level , rises to a constant rate r until it reaches a threshold value , at which point a response is
initiated. If r is randomly varied from one test to another, such as a Gaussian with mean μ and variance σ2,
the asymmetry of observed latency distributions is immediately explained. We consider three approaches:
LATER (Linear Threshold Approximation with Ergodic Rate) Model.
ELATER (Extended LATER) Model.
Fieller distribution with parameters κ, λ1, λ2, ρ.
2.1. LATER (Linear Threshold Approximation with Ergodic Rate) Model.
LATER [2], is a model originally derived empirically and vulnerable to experimental testing. Over the
last decade, we have been attempting to verify this functional interpretation by trying to challenge its three
elements:
S0 represents log prior probability. The change in reaction time is linearly related to the
logarithm of probability.
ST represents a threshold. The main part swivels about a fixed intercept. Reduction in latency is
associated with a large increase in the number of early responses.
r represents the supply of information. The rate of information supply affects the mean rate of
rise of the decision signal, and this turn causes the distributions not to swivel, but to be shifted
horizontally in a parallel fashion. We consider that r is a Gaussian variable with mean and
variance 2.
Time between the start and the threshold is:
Reciprocal of latency, 1/T:
Following that r is a Gaussian random variable, then, the distribution of 1/T is Gaussian with mean
and variance .
All biological systems are subject to unpredictable perturbations, technically known as noise. The sensorial noise does not contribute significantly to the variability of reaction time, according with a large
number of evidences. Neurophysiological experiments show that the contribution of randomness to the
overall variability of reaction time is insignificant. Suggestions such:
• LATER decision mechanism can be thought of as being preceded by a detection stage, obeying
random-walk dynamics.
• The observed randomness of reaction time does not originate in the outside world, it is deliberately
injected into the system from within. Agents try to be as unpredictable random as they possibly can.
The LATER is not a single model. Under specific conditions of experimentation, this model could be
combined into several instances with two or three LATER units [10]. Other approaches to the model
consider the existence of different prior probabilities of the R simulation, [11].
Carpenter [2] showed that the reciprocal of saccadic latency times (1/T) follows a normal distribution.
The Recinormal distribution of a random variable T is the distribution of the reciprocal , that is
normally distributed with mean and variance In Figures 1 and 2 we can observe the partial density function (PDF) and cumulative density function (CDF) of several examples of recinormal distribution for
several parameters of mean and variance. One of the most characteristics aspects of the recinormal
distribution is that it would be a bi-modal distribution. It always has exactly one positive mode and one
negative mode. Moreover, the density function is zero valued only at the origin. At this situation when we
16
consider only positive variables, the mode is unique, and the function is increasing from zero until the
maximum, and then is a decreasing function, [3], [4], [5], [6].
Figure 1: pdf of Recinormal Distribution.
- blue (µ = 0.005, σ = 0.01)
- red (µ = 0, σ = 0.01)
- yellow (µ = 0.02, σ = 0.01)
Figure 2: cdf of Recinormal Distribution blue
- blue (µ = 0.005, σ = 0.01)
- red (µ = 0, σ = 0.01)
- yellow (µ = 0.02, σ = 0.01)
2.2. ELATER Model
ELATER [9] model is an extension of LATER. The objective is to include trial-by-trial variability both
before and after sensory cues. In order to introduce some variability, we consider the existence of variations in
distance and the slope r between experiments. Now, we consider that both variables are independently, and
normality distributed and
. Latency distribution is determined by:
where,
,
and
.
In [9] several characteristics of the ELATER model are considered.
1) Mathematical proof that the slope variability can often become dominant in accounting for trial-by-trial
variability of the decision.
2) The conditions under which the ELATER model becomes equivalent to the LATER model.
3) The formula which describes the curve of the ELATER model on the reciprobit plot.
17
Figure 3: pdf ELATER distribution.
- blue (µr =1/ 30 , σr =0.005 , µ∆ = 10 , σ∆ = 2)
- red (µr =1/ 30, σr =0.005, µ∆ =10 , σ∆ = 1)
- green (µr =1/ 30, σr =0.005, µ∆ =10 , σ∆ =0.1)
- black (LATER model: µr =1 /300 , σr = 0.005)
Figure 4: cdf ELATER distribution
- blue (µr =1/ 30 , σr =0.005 , µ∆ = 10 , σ∆ = 2)
- red (µr =1/ 30, σr =0.005, µ∆ =10 , σ∆ = 1)
- green (µr =1/ 30, σr =0.005, µ∆ =10 , σ∆ =0.1)
- black (LATER model: µr =1 /300 , σr = 0.005)
2.3 Fieller Distribution Approach
Another approach [7] considers that RT will follow a distribution that is the ratio between two normally
distributed functions. And then, reciprocal of T, is a ratio between two distributions, too. The ratio of two
normally distributed variables follows the Fieller distribution, that presents different graphics (Fig. 5-7) as a
function of the values of the parameters of the two distributions.
We consider two random variables and
following a bi-variate normal
distribution with correlation coefficient ρ, then the ratio between follows a Fieller distribution:
,
where
,
and
, with ρ the Pearson correlation coefficient, then we have:
Value of Value of Distribution Ratio
0 0 Dirac( Any 0 (<0.22) N(
)
0 (<0.22) any ReciN
>0.443 >0.443 Cauchy
When the coefficient of variation of the two variables and are zero, the RT is constant. Then it follows
a distribution with all probability mass concentrated in one point (Dirac function). When is zero (or less than
0.22), then it follows a normal distribution with mean and variance ; the other case when is zero (or
18
less than 0.22), we have the ReciNormal distribution. Finally, when the two parameters and are both large
numbers (greater than 0.443) we have a Cauchy distribution (or Lorentz Distribution).
Figure 5: pdf: Fieller Distribution with
ρ=0.5, κ=0.2, λr=0.2, λΔ=2.5
Normal Distribution.
Figure 6:pdf: Fieller Distribution with
ρ=0.5, κ=5, λr=0.2, λΔ=2.5.
Recinormal Distribution
Figure 7: pdf: Fieller Distribution with
ρ=0.5, κ=0.5, λr=2.5, λΔ=0.75
Cauchy Distribution
19
3. Experimental Model:
The Early Years Toolbox (EYT) is a collection of freely accessible measures of young children’s emerging cognitive, self-regulatory, language and social development. Each measure is a brief, engaging,
game-like assessment that has been developed for the iPad. The experiment we are using is one from the
Toolbox (EYT) and is called Go/ΝoGo, [12]. This experiment consists of showing children a Fish or a
Shark on the iPad screen. Children have to select the fishes but not the sharks. There is a lot more fish than
there are sharks, so children get into the habit of tapping the screen, they need to overcome this habit
whenever they see a shark, the efficiency with which they can overcame that tap is our measure of
inhibition.
We have a Database with 250 children between the ages of 3 to 5 years old. Three-year-olds children
have only 1.5 seconds to respond when they see a fish, the older ones have 1 second but in the database,
we can have answers of these with 1 second or more. All time counts less than 300 ms where removed and
not considered for the mean. We separated the data analysis by age group and between the Go and NoGo responses and we haven´t considered the responses that exceed the timeout.
Once the frequency analysis was performed, we did the normality tests analysis and cleaned the
database by selecting only the correct answers, although we could have done a different analysis with all
data and including also the incorrect answers of the NoGo responses.
The distribution of our experiment has a mean of 0.79, variance of 0.017, asymmetry 0.963, kurtosis
1.891 and a significance value of 0.001 given by the Kolmogorov-Smirnov Normality Test (K-S Test).
Therefore, the distribution doesn´t follow a normal approximation (might be considered as a quasi-normal
distribution) and presents a high level of asymmetry.
The best fit of statistical distribution for Fig.8 - Distribution quasi-normal, is the theoretical distribution
of Fig.5 - Fieller Distribution, and the best option is the Cauchy distribution. Therefore, the values of the
two parameters and might be both greater than 0.443.
Figure 8: pdf: distribution quasi-normal but
presents a high level of asymmetry.
4. Discussion and Conclusion: This study is trying to explain the asymmetry of observed latency distributions. There are several
possibilities to make a significant contribution to these studies:
• Adjust the best distribution analysis for the real data:
• Fieller distribution implies linearity.
• Model LATER-d implies non-linearity.
• Recinormality assessment: The evaluation of the recinormality of the data sets by item will be provided by the analysis of the Reciprobit graphs.
20
• Separation of the effect stop-down of the bottom-up: distinguish between the variations of the
intercept
• Zone recinormal: This zone in Fieller Distribution corresponds to the normal and Recinormal cases. At this zone, we can use the common data analysis techniques under the assumption of normality.
This situation requires that the parameters and would be less than 0.22 (almost one of them).
• Cauchy zone: This corresponds to the value of parameters and greater than 0.443 (both of them). Between the recinormal and Cauchy zone, we have an intermediate zone where the distribution rapidly moves from normality towards Cauchy distribution.
• Experimental data could not be adapted to a specific distribution. Using the data of one experiment
for children into the range 3 to 5 years, Cauchy distribution would be the best option, but there are some other possibilities to be considered.
References: [1] Burle, B., F. V. C. T. T. H. (2004). "Physiological evidence for response inhibition in choice reaction time tasks". Brain and
Cognition, (56):153–164.
[2] Carpenter, R.H.S., Williams, M.L.L. (1995). "Neural computation of log likelihood in control of saccadic eye movements".
Nature, (377):59–62.
[3] Carpenter, R. (1981). "Oculomotor procrastination". D.F. Fisher, R. A. Monty J.W. Senders (Eds.), Eye Movements: Cognition
and Visual Perception, Hillsadale, New Jersey: Lawrence Erlbaum Associates, 237–246.
[4] Carpenter, R. (1999). "A neural mechanism that randomises behaviour". Journal of Consciousness, (6):13–22.
[5] Carpenter, R. (2000). "The neural control looking". Current Biology, (10):R291–R293.
[6] Carpenter, R. (2002)."Neurophysiology", 4th Ed.. London: Arnolds, London.
[7] Fieller, W. (1932). "The distribution of the index in a normal bivariate population". Biometrika, (24):428–440.
[8] Moscoso del Prado Martín, F. (2008). "A fully analytical model of the lexical decision task". B.
C. Love V. M. Sloutsky (Eds.) Proceedings of the 30th Annual Conference of the Cognitive Science Society, (30):1035–1040.
[9] Nakahara, H., K. N. . O. H. (2006). "Extended later model can account for trial-by-trial variability of both pre- and post-
processes". Neural networks, (19):1027–1046.
[10] Noorani, I, Carpenter, R.H.S. (2013) “Antisaccades as decisions: LATER model predicts latency distributions and error
responses”. European Journal of Neuroscience (37): 330-338.
[11] R Core Team (2017).R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing,
Vienna, Austria. Ratcliff, R. (1978).
[12] Howard, S. J.,Melhuish, E., & Chadwick, S. (2019). Early Years Toolbox (EYT), available in:
<http://www.eytoolbox.com.au/using-toolbox>. URL. Accessed 23rd
May 2019.
21
Effect of Job stress on job satisfaction in white collar-workers an
application of structural equation modelling
Batuhan ÖZKAN1 , Fatma NOYAN TEKELİ
2
1Yıldız Technical University, Faculty of Art & Science, Department of Statistics,
2Yıldız Technical University, Faculty of Art & Science, Department of Statistics, [email protected]
Abstract The aim of this study to analyze the effect of job stress on job satisfaction amaong the white-collar workers. Job satisfaction
as a pleasurable or positive emotional state resulting from the appraisal of one's job or job experiences. Job stress is a
condition of psychological distress felt by employees as a result of organizational stressors. Job stress can affect job
satisfaction and employee performance. The study used data of 243 white-collar workers in Turkey. To evaluate the data and
test the proposed model structural equation modelling was used. As a result of the study, It was seen that the increase in the
job stress of white-collar workers decreased the satisfaction of the job.
Key Words: job stress, job satisfaction, structural equation modelling
Introduction
The concepts of job satisfaction and job stress have been the subject of various researches due to their impact
on business performance. Job stress is a condition of psychological pressure which is vulnerable in a competitive
and volatile work environment. In addition to work environment, the demands and targets of the company, to be
achieved by the employees is also the main source of the cause of job stress. Job stress can affect the employee
performance. Excessive employee’s job stress should be avoided, as it can lead to a lot of absenteeism, errors in
work, low performance and loss of company reputation caused by uncomfortable work environment (Seňová and
Antošová, 2014). However, job stress, which can be handled well and still at low levels, can be a factor that
motivates employees to work better (Halkos and Bousinakis, 2010). Studies have shown that, employee performance is strongly influenced by job satisfaction and the levels of
job stress of the employee experiences. Recent studies obtained the findings that 50-60% of job stress is a major
cause of low employee performance (Choobineh, Ghanavati, and Hosseini, 2016). By the existence of the goals and objectives to be achieved by an organization, the employees must be able to adapt many demands in their
jobs. It can lead to stress for the employees. Long-term stress may overwhelm a person with demands that he/she
cannot meet, resulting in job dissatisfaction and a low performance (Robbins and Judge, 2017). By the existence
of the goals and objectives to be achieved by an organization, the employees must be able to adapt many
demands in their jobs. It can lead to stress for the employees. Long-term stress may overwhelm a person with
demands that he/she cannot meet, resulting in job dissatisfaction and a low performance (Robbins and Judge,
2017).
Excessive stress can increase job dissatisfaction (Reilly, Dhingra, and Boduszek, 2014). Job dissatisfaction
may relate with a number of dysfunctional outcomes including employee turnover, increased employee
absenteeism and declining employee performance (Kreitner and Kinicki, 2014). Job satisfaction involves
reaction or cognitive, effective and evaluative characters. Job satisfaction is a state of happy or positive emotions that comes from a person’s job assessment or work experience. Job satisfaction not only can reduce stress but
also helping improving performance, reducing employee turnover, and reducing absenteeism (Luthans, 2006).
An employee who gets job satisfaction will carry out his/her work well so that the performance will increase.
Meanwhile, an employee who does not get job satisfaction will be frustrated and it will affect the declining
performance.
In this study, it has been suggested in the proposed model that job stress has a negative effect on job
satisfaction. First, theoretical background is explained. Second, the conceptual model is proposed and the
methodology is described. Finally, the model is tested and results are presented with discussion.All of these
stages’ results showed that this the increase in the job stress of white-collar workers decreased the satisfaction of
the job.
22
LITERATURE REVIEW
Job Stress – According to Kreitner and Kinicki (2014), stress is an adaptive response, related to individual
psychological characteristics and/or processes, which are a consequence of any external action, situation, or
event that places a person’s psychological and/or physical demands.
Job Satisfaction – Locke in Luthans (2006) provides a comprehensive definition of job satisfaction that
includes cognitive, affective and evaluative reactions or attitudes which state that satisfaction is a pleasure or
positive feeling that comes from employee’s perception of how well their work is and is considered important.
The main factors affecting job satisfaction are: 1. The job itself, jobs that have the characteristics of challenging, not boring and support creativity can increase employee job satisfaction. 2. Wages, Employees view wages as a
reflection of how management values their contribution to the company. Wages that are not in accordance with
the given workload can trigger discontent from employees. In this study, the internal dimension of satisfaction is
discussed.
Methodology
In this section we discuss and develop the conceptual model. After that, we outline the sample and the
methodology and provide the results of the measurement and structural model
Proposed model
The proposed of model builds upon the several studies about the mental health, organisational works and
psychology. We test the proposed model introduced below on data collected by 243 white-collar employees in Turkey. The proposed model (Figure 1) that is tested in this paper consists of two major latent constructs: Job
satisfaction and job stress. To test the causal relationship between job satisfaction and job stress, the model
proposed on this study assumes that job stress is causally antecedent to job satisfaction. The model assumes
higher job stress produces lower job satisfaction
H1: Job stress has a direct effect on job satisfaction
Measures and Data
Under the headings of job satisfaction and job stress directed to the participant, it is aimed the measure the
internal satisfaction with the job and the stress created by the job. In order to measure internal satisfaction and
job stress, scales accepted in the literature were used. The Minnesota Job Satisfaction Scale and the Smith et al. and Quinn et al. Job Stress Scale were used. The number of indicators, their origin and measurement items of the
latent constructs are shown in Table 1.
As shown in Table1, all the indicators were measured on five-point scales that ranged from completely
disagree to completely agree. The means of the items ranged from 3.08 to 3.53, and all of them are higher than
the midpoint (2.5) of the ten-point scale.
23
Table 1. The number of indicators, their origin and measurement items of the latent constructs
Items Mean
Standart
Devaiation Kurtosis Skewness
Internal satisfac
tion ( The Minnesota Job Satisfaction Scale )
IS1 - I am always satisfied with my work.
3.5391 0.86335 -0.510 0.545
IS2 - I believe my job has a prestigious job in society. 3.5885 0.92452 -0.642 0.363
IS3 - I find the responsibility given to me in the workplace
satisfactory. 3.4527 0.95391 -0.411 -0.152
IS4 - I find my job to be sufficient in terms of the feeling of
doing something for others. 3.2798 1.12627 -0.359 -0.621
IS5 - I am satisfied with the authority I received in the direction
of other employees. 3.2016 0.96020 -0.499 0.010
IS6 - I work in a job where I can use my own ideas and
convictions. 3.2757 1.02152 -0.293 -0.248
Job stress (Smith et al. and Quinn et al. Job Stress Scale)
JS1: I am under constant time pressure due to a heavy workload 3.0864 1.18389 -0.138 -0.793
JS2: I have very little freedom to decide how I do my work 3.5309 1.05728 -0.473 -0.261
JS3: Considering the things I have to do at work, I have to
work very fast 3.3539 1.11259 -0.335 -0.533
JS4: I often feel bothered or upset in my work 3.2757 1.15802 -0.264 -0.743
JS5: The demands of my job interfere with my personal life. 3.2963 1.10346 -0.311 -0.530
As shown in Table 2, of that 55.1% of the subjects who participated in the survey were woman, 44.9% were
man. According to their ages, 49% of the participant were between the ages 20-30; 28 % were between 31-
40;18.13% were between 41-50; 4.9% at the age 51 or over. As far as their experience is concerned, 22.2% of
them had less than 1 year experience; 42 % had 1-5; 11.1% had 6-10; 24.7% had 11 years and over experience.
According the their sector, 81.1% of the participant were worked in private sector; 18.9% were worked in public
sector.
24
Table 2. Demographic profile of the respondents
n(243) %
Gender
Female
Male
134 55.1
109 44.9
Sector Type
Private Sector 197 81.1
Public Sector 46 18.9
Experience
Less than 1 year 54 22.2
1-5 102 42.0
6-10 27 11.1
11 years and over 60 24.7
Age
20-30 119 49.0
31-40 68 28.0
41-50 44 18.1
51 and over 12 4.9
Findings And Discussions
The statistical analyses were realized by using Mplus 6.1 packaged software.
Exploratory factor analysis (EFA) Before testing the proposed relationships between factors, the data set is used to derive a factor model by EFA
and subsequently test this model by Confirmatory Factor Analysis (CFA). Factor loadings and cross loadings for
scale items, eigenvalue, and explained variance for factors were examined using EFA. Before factor analysis,
KMO Sample Adequacy Test and Bartlett Sphericity tests were applied. The value of the KMO Measure of
Sampling Adequacy is 0.861 (should be larger than 0.5) indicating factor analysis is appropriate. Bartlett’s test of
sphericity was rejected (p=.000) to conclude that there are correlations in the data set that are appropriate for
factor analysis. It is concluded that the data is suitable for factor analysis. By considering alternative solutions, the study identified the best structure as a two-factor solution. In this study, two factor were extracted using
Principal Components Factoring with Promax rotation. The two constructs are unidimensional as only the first
eigenvalues for each construct are greater than one using the criterion “eigenvalues greater than one” in the
Kaiser’s method (Guttman, 1954; Kaiser, 1960). Promax rotated factor loadings are presented in Table 3. An
examination of the factor loadings showed that the items under each factor seemed to be highly loaded onto the
relevant factor. Therefore, these 2 factors, which were obtained from the factor analysis, and the items of factors
best served the purpose of the research, described the measurement model in the best way and explained 65.71%
of the total variance. According to the factor loadings and cross loadings, a total of 11 items were included in the
measurement model to examine the job satisfaction of white collar-workers.
25
Confirmatory factor analysis (CFA) To select the estimation method of CFA, we examined our 11 items in terms of their skewness and kurtosis,
as shown in Table 1. The skewness and kurtosis values of the items are in the interval of (-.1; -1). According to
Lei and Lomax (2005), if the absolute values of these two values are below 1.0, the deviation from normality is
defined as slight; moderate is between 1 to 2.3, and severe is above 2.3. There are slight deviations from
normality for the items that are used to measure the constructs, and we conclude that the data set closed to a
normal distribution (Lee, Ooi, Tan, & Chong, 2010; Ooi, Cheah, Lin, & Teh, 2012; Zhang, 2000). Maximum
likelihood (ML) is widely used in normal-theory estimation procedures (Fan, Wang, & Thompson, 1997). CFA
was conducted using ML estimation to confirm the measurement model with 2 latent variables. The
measurement model fit results showed a good fit to the data according to Hu and Bentler (1999)’s two-index strategy, which suggests to use a combination of (SRMR) value ≤ 0.09 and (RMSEA) value ≤ 0.06, or (NNFI)
value ≥ 0.96 and a SRMR value ≤ 0.09, or (CFI) value ≥0.96 and a SRMR value ≤0.09. In accordance with the
SRMR and RMSEA combination of this strategy, measurement model fit was acceptable with the values of
SRMR= 0.04 and RMSEA = 0.06. The other fit indexes also had acceptable levels such as normed 2 / df =
2.146, p-value for test of close fit (RMSEA < 0.05) = 0.92, CFI = 0.98, and NNFI= 0.98. The estimated factor
loadings should be significant and the signs of them should be consistent with the theory. All factor loadings of
the items in this model were statistically significant at the 0.01 level (t-values >2.58), and standardized factor
loadings were greater than 0.7.
Table 3 : Loading Factor, Average Variance Extracted (AVE) Value and Cronbach’s
Construct Items Factor Loading AVE Cronbach
Job stress JS5 0.892
0.801 0.928
JS3 0.871
JS4 0.842
JS2 0.816
JS1 0.749
Internal Satisfaction IS6 0.816 0.735 0.830
IS5 0.770
IS3 0.753
IS1 0.623
IS2 0.581
IS4 0.572
Standardized factor loadings greater than 0.70 provide evidence for convergent and disciriminant validity
(Anderson & Gerbing, 1988). Average Variance Extracted (AVE) and Cronbach's values are presented in
Table 3. Convergent validity is assessed by the magnitude and significance of the factor loadings of each
indicator of the latent factors. Convergent validity is sufficient when AVE is greater than 0.50. Cronbach's
(Cronbach, 1951) is used to assess reliability and it takes values between 0 and 1. As shown in Table 3, all the
AVEs exceed the recommended level of 0.50. These values indicate convergent validity. All reliabilities ( )
exceeded the recommended level of 0.70.
26
Structural equation modeling (SEM)
Full structural equation model was estimated imposing the hypothesized relationships shown in the Figure 1
to measurement model.
Fig. 1. SEM model
To assess SEM model fit, calculated values of goodness of fit indexes were compared to the recommended
levels using some thumbs of Schermelleh-Engel et al. (2003), fit indices, and acceptable thresholds of Hooper et
al. (2008) and strategies of Hu and Bentler (1999). The structural model fit results showed a good fit to the data
according to Hu and Bentler (1999)’s two-index strategy, which suggests to use a combination of (SRMR) value ≤0.09 and (RMSEA) value≤0.06, or a non-normed fit index (NNFI) value ≥0.96 and a SRMR value ≤0.09, or
(CFI) value ≥0.96 and a SRMR value ≤0.09. In accordance with the SRMR and RMSEA combination of this
strategy, structural model fit was acceptable with the values of SRMR =0.04 and RMSEA =0.06. The other fit
indexes also had acceptable levels such as normed, 2 / df = 2.146, p-value for test of close fit (RMSEA < 0.05)
=0.50, CFI =0.98, and NNFI =0.98.
For classical hypothesis testing, the significance of a path is assessed by the p value (in general, p < 0.05),
standard coefficient, standard error, t and p values are shown that the paths are significant. The hypothesis
testing result (p value= 0.002) are supported that job stress had direct negative effects on job satisfaction.
Regarding the R2, 47.0 % of the variance in job satisfaction was explained by the job stress. In this study, after building the measurement model for the latent variables of job stress and customer
satisfaction, the relationships between these two constructs are empirically examined for Turkish white collar-
workers using the data obtained from 243 employees via questionnaire. Structural Equation Modeling (SEM)
was performed in order to test all the relationships among variables in the proposed model. Based on the results
of the hypothesis test, it is known that there is a negative and significant effect of job stress toward job
satisfaction. These findings indicate that when job stress is at the low level, it can decrease employee job
satisfaction. This supports the research conducted by Hanafi and Ulfa (2018), Khamisa et al. (2017), Ramos,
Alés, Sierra (2014), Khalatbari, Ghorbanshiroudi, & Firouzbakhsh and Trivellas, Reclitis, & Platis (2013) who
mentioned that job stress had a negative and significant effect on employee job satisfaction. Based on the results
of research that has been described and discussed in the previous, it can be concluded as follows: Job stress
negatively affects the job satisfaction of white-collar workers.
27
According to Robbins and Judge (2017), in an organization there are several factors that may cause stress
including: (a) task demands that include the design of individual work (autonomy, task diversity, degree of
automation), working conditions, and physical layout of work; (b) role demands relating to the pressure that a
person exerts as a particular function he or she plays in the organization. Role conflict creates expectations that
may be difficult to complete or meet. Excessive workload and too little workload are stress generators; (c)
interpersonal demands are pressures created by other employees in the organization. Unclear communication
between one employee and others will lead to unhealthy communication. In future studies, work stress can be
considered within the framework of the dimensions described above. Thus the effects of all dimensions can be
seen separately. This method can be more useful for increasing job satisfaction.
References
[1]Amoako, E. P., Gyamfi, O. A., Emmanuel, A. K., & Batola, D. (2017). The Effect Of Occupational Stress On Job Performance At ASPET
A. Company Limited. Global Journal of Arts, Humanities and Social Sciences, 5(8), 1–17.
[2]Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A review and recommended two-step approach.
Psychological Bulletin, 103(3), 411–423.
[3]Arshadi, N., & Damiri, H. (2013). The Relationship of Job Stress with Turnover Intention and Job Performance: Moderating Role of
OBSE Procedia – Social
and Behavioral Sciences, 84(2003), 706 –710.
[4]Azman, I., Noorshafine, S., Ismail, Y., Jauhariah, A., Samah, A., Bakar, R. A., Aminudin. (2015). Effect Of Workplace Stress On Job
Performance, Xiii(1).
[5]Bakotić, D. (2016). Relationship Between Job Satisfaction and Organisational Performance. Economic Research-Ekonomska Istraživanja,
29(1), 118–130.
[6]De Simone, S., Cicotto, G., & Lampis, J. (2016). Occupational Stress, Job Satisfaction and Physical Health in Teachers. Revue
Européenne de Psychologie Appliquée/European Review of Applied Psychology, 66(2), 65–77.
[7]Guttman, L. (1954). Some necessary conditionsvfor common-factor analysis.vPsychometrika, 19(2),149–161.
[8]Halkos, G., & Bousinakis, D. (2010). The effect of stress and satisfaction on productivity. International Journal of Productivity and
Performance Management, 59(5), 415–431.
[9]Hanim, Maslatifa. (2016). Pengaruh Stres Kerja Terhadap Kinerja Karyawan Dengan Kepuasan Kerja Sebagai Variabel Intervening.
Jurnal Ilmu Manajemen Volume 4 Nomor 3 - Jurusan Manajemen Fakultas Ekonomi Universitas Negeri Surabaya
[10]Hooper, D., Coughlan, J., & Mullen, M. (2008). Structural equation modeling: Guidelines for determining model fit. Electronic Journal
of Business Research Methods, 6(1), 53–60.
[11]Hu, L.-T., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin,
112(2), 351–362.
[12]Hoboubi, N., Choobineh, A., Kamari Ghanavati, F., Keshavarzi, S., & Akbar Hosseini, A. (2017). The Impact of Job Stress and Job
Satisfaction on Workforce Productivity in an Iranian Petrochemical Industry. Safety and Health at Work, 8(1), 67–71.
[13]Inuwa, M. (2016). Job Satisfaction and Employee Performance: an Empirical Approach. Themillenniumuniversity.Edu.Bd, 1(1), 90–103.
[14]Jogianto, Hartono dan Abdillah. (2015). Partial Least Square (PLS)-Alternatif Structural Equation Modeling (SEM) Dalam Penelitian
Bisnis, Yogyakarta : Penerbit Andi
[15]Kadir, A. R., Kamariah, N., & Saleh, A. (2017). The Effect Of Role Stress, Job Satisfaction, Self-Efficacy And Nurses’ Adaptability on
Service Quality in Public Hospitals of Wajo. International Journal of Quality and Service Sciences, 9(2), 184–202.
[16]Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20(1),
141–151.
[17]Khalatbari, J., Ghorbanshiroudi, S., & Firouzbakhsh, M. (2013). Correlation of Job Stress, Job Satisfaction, Job Motivation and Burnout
and Feeling Stress. Procedia - Social and Behavioral Sciences, 84, 860–863.
[18]Khamisa, N., Peltzer, K., Ilic, D., & Oldenburg, B. (2017). Effect of Personal and Work Stress on Burnout, Job Satisfaction and General
Health of Hospital Nurses in South Africa. Health SA Gesondheid, 22, 252–258.
[19]Kreitner, Robert; Angelo Kinicki. (2014). Perilaku Organisasi, Jakarta : Salemba Empat.
[20]Kusuma, Cahya., Raharjdo, Kusdi., Prasetya, Arik. (2015). Pengaruh Stres Kerja dan Kualitas Kehidupan Kerja terhadap Kepuasan
Kerja dan Kinerja Karyawan (Studi pada Karyawan Non Medis Rsud Ibnu Sina Gresik). Jurnal Administrasi Bisnis. 18(1): 1-9.
[21]Lei, M., & Lomax, R. G. (2005). The effect of varying degrees of nonnormality in structural equation modeling. Structural Equation
Modeling,12(1), 1–27.
[22]Luthans, Fred. (2006). Perilaku Organisasi. Yogyakarta : Penerbit Andi
[23]Malthis, Robert, L. Jhon Jackson. (2006). Manajemen Sumber Daya Manusia. Jakarta : Salemba Empat
[24]Platis, C., Reklitis, P., & Zimeras, S. (2015). Relation between Job Satisfaction and Job Performance in Healthcare Services. Procedia -
Social and Behavioral Sciences, 175, 480–487.
[25]Ramos, A., Borrego-Alés, Y., & Mendoza-Sierra, I. (2014). Role stress and work engagement as antecedents of job satisfaction in
Spanish workers. Journal of Industrial Engineering and Management, 7(1), 360–372.
[26]Reilly, E., Dhingra, K., & Boduszek, D. (2014). Teachers’ Self-Efficacy Beliefs, Self-Esteem, and Job Stress as Determinants of Job
Satisfaction. International Journal of Educational Management, 28(4), 365–378.
[27]Robbin s, Stephen P; Timothy A.Judge. (2016). Perilaku Organisasi, Jakarta : Salemba Empat
[28]Seňová, A., & Antošová, M. (2014). Work Stress as a Worldwide Problem in Present Time. Procedia - Social and Behavioral Sciences,
109, 312–316.
[29]Sugama. (2016). Pengaruh Stres Kerja Dan Motivasi Ter-Hadap Kinerja Pegawai Melalui Kepuasan Kerja Sebagai Variabel Intervening
Pada Unit Layanan Pengadaan (ULP) Provinsi Bali. Jurnal Ekonomi & Bisnis, Vol. 4, No 1. Maret 2017, Hal 11-26.
[30]Şimşek, G. G., & Tekeli, F. N. (2015). Understanding the antecedents of customer loyalty by applying structural equation modeling. In
U. Akküçük (Ed.), Handbook of research on developing sustainable value in economics, finance, and marketing (pp. 420e445). Hershey,
PA: IGI Global.
[31]Trivellas, P., Reklitis, P., & Platis, C. (2013). The Effect of Job Related Stress on Employees’ Satisfaction: a Survey in Health Care.
Procedia - Social and Behavioral Sciences, 73, 718–726. Yozgat, U., Yurtkoru, S., & Bilginoğlu, E. (2013). Job Stress and Job
Performance Among Employees in Public Sector in Istanbul: Examining the Moderating Role of Emotional Intelligence. Procedia -
Social and Behavioral Sciences, 75, 518–52
28
A CREDIT DEFAULT SWAP APPLICATION BY USING QUANTILE REGRESSION
TECHNIQUE
Assoc. Prof. Dr. Yüksel Akay Ünvan
Prof. Dr. Hüseyin Tatlıdil
Ankara Yıldırım Beyazıt University,
Faculty of Management, Banking and
Finance Department, Turkey
Hacettepe University, Faculty of Science,
Department of Statistics, Turkey
[email protected] [email protected]
ABSTRACT
The growing global financial environment continues to develop new financial
instruments and thus respond to customers' different quests. A credit default swap (CDS) is a
type of financial derivative or contract that permits an investor to swap or balance the owned
credit risk with that of another investor. Recently this investment tool has been preferred by a
wide range of investors in order to minimize their probability of credit default. In this respect,
many economists and researchers agree that credit default swaps contribute significantly to
the prevention of credit risk.
Data size and complexity are increasing in research and business analyse. This
situation emphasizes the importance of easily applicable, reliable and measurable techniques
for estimation and identification. Quantile regression model comes into play at this point by
providing conditional quantiles of solutions with a general linear model that assumes non-
parametric form for the conditional distribution of the solutions. Moreover, it is possible to
obtain more information by this method which could not be reached directly from standard
regression methods. Furthermore, quantile regression method has a broad application area in
various disciplines since it gives the option of modeling the tails of the conditional
distribution. In this study, a compherensive literature review was given at the begining and
then a credit default swap application was implemented by using the quantile regression
method. In the application section, the Credit Default Swap variables and the ratings of
various international independent rating agencies such as Standard & Poor’s, Fitch, and
Moody’s of Turkey were used for the last six years.
Key Words: Credit Default Swap, Quantile Regression, Credit Risk.
29
1. INTRODUCTION:
With its growing knowledge and the ever-growing market, the global financial
environment produces new financial tools to meet the changing needs of the demanders.
Credit Default Swap (CDS) is a type of financial derivative or contract that allows an investor
to swap or balance the credit risk of another investor. Recently, this investment tool is
attracted by investors for the purpose of minimizing the probability of credit default and thus
reducing the owned risk factor. In this context, many experts from different disciplines
support that credit default swap transactions significantly contribute to the mitigation of credit
risk.
The increasing complexity of data requires versatile methods of building statistical
models. That is the need for more reliable and efficient techniques to be used in data
prediction and determination processes has been raised. Quantile regression model gains
importance at this stage since the method presents conditional quantiles of solutions with a
general linear model that accepts non- parametric form for the conditional distribution of the
solutions. Moreover, it is possible to get more information by using this method compared to
standard (ordinary) regression methods. Furthermore, the quantitative regression method has a
wide range of applications in various disciplines to explain the conditions for modeling the
queues of conditional distribution. In this paper, a literature review was given firstly, and then
an application of quantitative regression method using credit default swap data was generated.
In the application section, Credit Default Swap variables and ratings of international
independent organizations such as Standard & Poors, Fitch and Moody’s of Turkey were used
for over the past six years.
2. CREDIT DEAFULT SWAP:
Credit derivatives are exciting innovations in financial markets. They give the potential to
companies to trade and manage credit risk. The most popular credit derivative is a credit
default swap. In 1997, a credit derivative team at JP Morgan’s (New York City, USA)
launched CDSs with newspaper articles. At that time, they named this new derivative type as
BISTRO (not CDS) which stands for Broad Index Secured Trust Offering. This product was a
later stage in the development of CDS trading and the credit derivative market (Levy, 2009).
There are different kinds of credit default swaps: Binary credit default swaps, basket credit
default swaps, contingent credit default swaps, and dynamic credit default swaps (Hull &
White, 2000). David Mengel (2007) describes evolution of CDS market from 1980 until today
in four stages in his overview of credit derivative market. The first stage of the credit
derivative trading can be characterized as a defensive step. It mainly includes attempts taken
by major banks to eliminate some of the credit exposure on their balance sheets. This stage
took place in the late 1980s and early 1990s. During this period, banks had sold their loans to
the other banks or private investors in return for periodic payments by using product similar to
CDSs. When default happened, similar to the CDS contract, the loans or bonds that have
credit exposure were being delivered to the investor, who would take the losses instead of the
bank. The second stage took place between 1991 and the late 1990s. The main change during
this stage is the development of financial engineering technology for pricing the transfer of
credit risk. The third stage is the mature CDS market which exist today and the
standardization of its trade and contractual terms. During this stage, single name CDS
30
contracts were developed and started being traded Over-The Counter (OTC). Moreover, some
new regulations were developed to organize and guide trade and define capital requirements.
The International Swaps and Derivatives Association (ISDA) introduced the standardized
contractual agreement, which offers the standard CDS agreement accepted by most of the
traders today. Counterparty risk management begins with ISDA or other related transaction
documentation. This is followed by measurement of both current exposure and potential
losses if default were to occur in the future and finally collateral net exposures are made
(Chaplin, 2005). The fourth stage is the expansion of the types of players engaged in trading
in the CDS market. This stage saw the entry of hedge funds as major players into CDS
market. Hedge funds started to take the position of sellers or buyers, based on seeking
exposure or hedging the credit risk. Hedge funds are now using CDSs to trade misprices in
credit risk, to remove unwanted credit risk from their portfolio and to trade CDS bond basis
spreads. This fast dynamic hedge fund activity in the CDS market has contributed to increased
trade volume and increased liquidity which has resulted in better price discovery (Mengle,
2007).
A credit default swap contract provides insurance against default. Most CDS protect
against default of high-risk municipal bonds, sovereign, corporate debt, the credit risk of
mortgage-backed securities, junk bonds, and collateralized debt obligations. The credit default
swap is the building stone of hedging strategies for credit exposures. The buyer may default
on the contract, thereby denying the seller the expected revenue. The seller transfers the CDS
to another party but it may lead to default. Where the original buyer drops out of the
agreement, the seller may be forced to sell a new CDS to a third party to recoup the initial
investment. However, the new CDS may sell at a lower price than the original. CDS, leading
to a loss. It is a contract between protection buyer and protection seller. The protection buyer
is compensated for any loss emanating from a credit event in a reference instrument. The
protection buyer makes periodic payments to the protection seller. In a credit default swap,
the protection buyer makes a payment (a fee), called swap premium, to the protection seller.
In the end there exists the right to receive a payment depends on the default of the reference
entity. The payments made by the protection buyer are called the premium leg; the contingent
payment that might have to be made by the protection seller is called the protection leg
(Fabozzi, 2001). CDS are the most widely used type of credit derivative. The development of
CDS products has led to the increasing attention of investors in these products. They are
interested in the factors that can affect CDS spreads. A CDS is a swap contract in which the
contract buyer pays a series of payments to a seller in exchange for protection from default in
the reference entity (Yang, Morley, & Hudson, 2010: 2). CDS spreads are leading indicator of
creditworthiness. Sovereign CDSs constitute a minor though growing part of the CDS market.
The CDS market has grown over the last decade and has thus become more prominent in
finance literature (Galil, Shapir, Amiram, & Ben-Zion, 2014: 271). The quality of government
institutions affects the likelihood of sovereign default. This enhances a country’s willingness
to repay debt, and so reduces the probability of sovereign default. A change in the credit risk
of a sovereign borrower reflected in its sovereign CDS spread can thus be considered an
indicator of the country's economic-political stability, which is linked to country-specific
macro-economic variables such as output growth, foreign Exchange reserves, budget deficit,
real effective exchange rate deviation, and foreign direct investment (Hui & Fong, 2015 :
174).
31
3. QUANTILE REGRESSION:
The idea of predicting the median regression slope was suggested by Ruđer Josip
Bošković in 1760 as a fundamental theorem for minimizing the sum of the squares of absolute
deviations and as a geometric algorithm to create a median regression (Stigler, 1984). And he
produced the first geometric procedure from three observations of a surface property to
determine the equator of a rotating planet. This was followed by OLS (Ordinary Least
Squares) found by Legendre in 1805 (Furno & Vistocco, 2018).
In the following periods, Bošković's ideas began to be developed. Francis Edgeworth
has found the plural media (Koenker, 1998) - a geometric approach to the median regression-
and accepted as the pioneer of the simplex method. Roger Koenker's works of Bošković,
Laplace and Edgeworth have been accepted as a preliminary preparation for his contributions
to QR (Quantile Regression). Since the early 1950s, it has been accepted that median
regression methods based on minimizing the sum of squares of absolute residuals can be
formulated as linear programming problems and can be solved efficiently with a form of
simplex algorithm (Furno & Vistocco, 2018).
Koanker and Bassett developed the Slice / Quantitative Regression-D / KR (Quantile
Regression-QR) method approach in 1978, which is a statistical model for estimating
conditional slice functions. The basic logic is to model conditional slices as a function of
independent variables. The traditional regression model tries to explain the changes in the
conditional mean of the dependent variable; slice regression describes changes in conditional
slices. In this respect, it is more flexible than the traditional regression. Because it gives
important information about how the distribution of dependent variable is affected by
independent variables, it has found wide use in social sciences.
Quantile Regression (QR) models, which are widely used in economics, are used for
estimation of conditional mean functions and conditional quantile functions. QR is the
generalized version of Lad Regression for the specified quantiles. These regression models
are less sensitive to outlier values and abnormalities than OLS method (Kurtoğlu, 2001, p.15).
The QR is especially useful in situations where conditional quantiles vary. Moreover, the
method determines the regression coefficients depending on quantiles (Chen, 2005).
The OLS method is usually used to estimate the value of the parameters. With regard to
this method, a well-documented and comprehensive test methodology in most statistical
packages is obtained if the normality assumptions are omitted. The principle of this method is
to minimize the sum of the squares of the error. However, in this method, the errors should be
distributed normally, they should not contain outliers and the error variances should be
homogeneous. The OLS method cannot be applied if one of these conditions is not provided.
If one or more of the assumptions are not fulfilled, the results may be misleading (Ferra,
Hazmira & Izzati, 2016). However, most data are not inherently homogeneous. Therefore, the
need for an alternative approach to Classical Linear Regression was felt and QR was
developed at this point. QR is also a robust approach when the limitations discussed above are
available for an ordinary OLS estimator because the quantile method is a method of
regression modeling by dividing a data group into pieces after the data is sorted from the
smallest to the largest (Arbia, 2006). In the quantile method, the normality assumptions are
violated. There is no outlier value and homogeneity is not required. This method uses the
parameter estimation approach by assuming the conditional quantization function in the
distribution of the data, minimizing the absolute asymmetry of the asymmetric weighted error
32
and minimizing the absolute asymmetry in the distribution of the data, and dividing the data
into quantities (Feng & Zhu, 2016). Both Ordinary Least Square (OLS) and Quantile
Regression (QR) models are estimation techniques used to estimate the coefficients equation
in the Linear Regression Model.
Finally, for some error distributions (eg long tails), the QR estimator
,is more efficient
than the OLS estimator
.
is only efficient in the class of linear neutral estimators.
This is the main motivation that Koenker recommends to use QR in a variety of environments
instead of OLS. If the distribution of errors is normal,
is more efficient than
(Koenkar
& Bassett, 1978). One of the major differences between the OLS method and QR is that the
average is more affected from outlier values and other extreme data. The disadvantage is that,
if all the assumptions are met, it is less efficient, ie the estimates are less sensitive.
4. CREDIT RATING AGENCIES:
Credit risk ratings and CDS spreads are the important indicators of credit risk. This study
investigates the relationship between credit risk ratings and sovereign CDS spreads. If credit
rating announcements have new information, CDS spreads are expected to respond to the
corresponding new risk level. In order to measure issuer’s relative credit worthiness, CRAs
offer a variety of ratings, outlooks and reviews for different debt instruments. Today, credit
rating agencies are the major institution providing information on securities’ relative
creditworthiness and ability to obey contractual and financial obligations when they become
due (Poon & Chan, 2010). These credit ratings categorize the entities according to their
likelihood of failure to pay obligations and the loss in the event of default (Crouhy, Galai, &
Mark, 2001). Credit Rating Agencies (CRAs) such as Standard & Poor’s (S&P), Moody’s and
Fitch are the leading providers of credit ratings and credit risk analysis and claim forward
looking opinions about credit risk. Although there are over 150 rating agencies, the three
before mentioned agencies represent 95% of the total market for rated credits (White, 2010).
The most influential credit rating agencies today are Standard and Poor’s, Moody’s and Fitch
(Micu, Remolona, & Wooldridge, 2004). At the sovereign level for the developed economies,
Afonso et al. (2011) found evidence for significant spread reaction to positive rating
announcements by S&P and negative rating announcements by Moody’s. For the emerging
economies at the sovereign level, the positive rating announcements are found to have
significant impact on CDS spreads while the negative rating announcements are found to have
no impact (Ismailescu & Kazemi, 2010).
The main function of credit rating agencies is to determine the ability of the
borrower to pay the debts and the risks that affect this power, and to monitor their change
over time. The rating is made on a national basis for national borrowings while it can be made
for countries, financial institutions, mutual funds and non-financial companies for
international borrowings. Credit rating should help investors make the right decision. For this
reason, the rating process should be based on accepted objective criteria recognized by all
relevant sectors, should be comparable, and should not be subject to unidentifiable and
incomprehensible subjective effects, especially to internal and external political interventions.
Credit rating is closely related to the behavior of the banking sector. BASEL regulations that
banks must comply with, risk management credit rating results over credit systems as an
indicator. These applications also applies to our country (Aydın, 2018).
33
The role of credit rating agencies in the markets has gained importance with the
globalization that started in the 1980s. A number of credit ratings today operating on a global
level and the three most important rating agencies are S & P, Moody’s and Fitch. According
to the notes given by these organizations, countries and companies can give or borrow debt.
The notes given by these institutions provides both information to investors and the ease of
borrowing for countries and firms by measuring the risk of loans (Yıldırım et al., 2018).
The following table shows that the evaluation criteria of these three rating agencies. The
ratings used in the application section are based on this noting system.
Table 1. Credit Rating Note System of Agencies
Standart & Poor’s
Fitch Moody’s Note Explanation
AAA AAA Aaa Highest Credit Degree
Investment Level
AA+ AA+ Aa1 Good Credit Degree
AA AA Aa2
AA- AA- Aa3
A+ A+ A1 Good Credit Degree
A A A2
A- A- A3
BBB+ BBB+ Baa1 Level Below Middle
BBB BBB Baa2
BBB- BBB- Baa3
BB + BB + Ba1 No investment
Speculative Level
BB BB Ba2
BB - BB - Ba3 Speculative B+ B+ B1
B B B2 Significant speculative B- B- B3
CCC+ CCC Caa Severe Risky CCC CC Caa3
CC C C Extreme speculative
D DDD DD D
D Can't Fulfill Obligation
Default
34
5. APPLICATION
5.1. Statistical Analysis:
5.1.1. Some Descriptive Statistics of Variables
Table 2 shows the mean, median, maximum, minimum and standard deviation values
for each variable used in the study. Since the CDS variable was calculated instantaneously,
there was quite a difference between the maximum and minimum values. However, since
Fitch, Moody’s and S & P variables are calculated annually, the difference between maximum
and minimum values is much less. Moreover, since Fitch organization gave the note BBB-
corresponding to 55.18% to Turkey between the years 2012-2016, the median and maximum
value for the variable Fitch are the same. In other words, the median value that is the most
repetitive and naturally closer to the mean is also the maximum value.
Table 2. Descriptive Statistics
CDS FITCH MOODY’S S&P
Average 231,9807 52,85139 50,96083 46,00389
Median 218,4990 55,18000 53,52000 48,54000
Maximum 558,3720 55,18000 55,18000 50,20000
Minimum 117,8090 43,56000 38,58000 35,26000
Standard
Deviation 70,06720 3,520397 4,430987 4,113339
5.1.2. Correlation Analysis
The relationship between the variables used in the study will be examined with the
help of correlation coefficient. Correlation coefficient refers the relation between two
variables. This coefficient is between -1 and +1 and it is not possible to go beyond these
limits. If the correlation coefficient is equal to 1, we can say that there may be 100% positive
relationship between these two variables and 100% negative relationship if it is equal to -1.
Generally, 50% or less correlation is defined as a weak relation. The Pearson correlation
coefficient is found by the following formula and the correlations of all variables in a model
are shown in the correlation matrix. The values in the correlation matrix can not be greater
than 1 and not less than -1. Also the diagonal values are always equal to 1.
i= 1,…., n = sample size, (1)
Source: https://www.mathsisfun.com/data/correlation.html
In this formula, x and y are the two variables whose correlation coefficient will be found. The
other variables in the formula are explained as follows.
= ith
observation in x variable.
= yth
observation in y variable
35
When Table 3, which is the tabulated form of the correlation matrix, is examined, it
is sufficient to interpret only the upper or lower part of the diagonal since it is always in the
symmetry state. As seen in the table, there is a negative relationship between CDS and all
remaining variables. The CDS has a negative relationship with Fitch, Moody’s and S & P
evaluation institutions, respectively, with 55.18%, 56.06% and 57.46% negative relations. As
a general conclusion, it can be said that the increase in positive or negative direction of these
evaluation institutions will cause a reverse movement in CDS.
Table 3. Correlation Coefficients
Variables CDS FITCH MOODY’S S&P
CDS 1,0000 -0,5518 -0,5606 -0,5746
FITCH -0,5518 1,0000 0,9511 0,9319
MOODY’S -0,5606 0,9511 1,0000 0,9506
S&P -0,5746 0,9319 0,9506 1,0000
5.1.3. Augmented Dickey Fuller (ADF) Test:
In the studies conducted with time dependent variables, the stability must be looked at
firstly. The variables that are used without being stabilized can give misleading results.
Augmented Dickey Fuller (ADF) Test, which is one of the most common methods, was used
for this purpose. For the ADF Test, assume that is a random walk operation. When is
removed from both sides of the regression equation ( =ρ + ); the equation of ∆ = π
+ Y (t-1) + εt is obtained.
Here where π = (1 - ρ),
ε_t = refers to the probabilistic error term with constant variance and non-zero average,
providing assumptions,
Y = refers to the coefficients of the time series. The hypothesis to be applied for the test
is as follows:
: π=0 (Yt is not stationary, so it has unit root. )
: π<0 (Yt is stationary, so it has not unit root)
In the case of π = 1, Yt has a unit root (Gujarati, 2005, s.718). A time series with a unit
root is random and not static. In this model, π was tested with the unilateral t Test. If Yt is a
static variable, it is possible to apply standard tests for π (Sjö, 2008, p.4).
This study was carried out with time dependent variables including monthly data
between 2013-2018. Analysis with time-dependent variables requires a stabilization first.
Augmented Dickey Fuller (ADF) Unit Root Test, which is one of the most common methods,
was performed for this aim. Firstly, this test was applied for the variables by Fixed and Fixed
+ Trend models separately (raw data) without taking difference. Since the probabilistic values
of all variables are greater than 0,05, the hypothesis “ : The variable is not stationary, so it
has unit roots” is not rejected. There is no stability for all variables. Therefore, the first
difference of the variables was taken and the same test was performed again. Since the
probability values of all variables are less than 0,05, the hypothesis is rejected this time.
Thus, the stabilization process is completed.
36
Table 4. ADF Test
Variables Probability Values Before
Difference
Probability Values After
Difference
Type of Model Fixed Fixed+Trend Fixed Fixed+Trend
CDS 0,3900 0,4827 0,0001 0,0000
FITCH 0,9862 0,8609 0,0000 0,0000
MOODY’S 0,9961 0,8389 0,0000 0,0000
S&P 0,9573 0,1852 0,0000 0,0000
5.1.4. The Regression with Least Squares Method
The univariate regression equation is the following; and are the parameters in the
mass regression equation, 0 and 1 are the estimations from the sample.
(2)
The Least Squares Method as the name suggests, is the method of forming the
regression model with the value that makes the estimation values of the sampling parameters
of 0 and 1, the sum of the square of the deviations, the smallest (Alma and Vupa, 2008,
p.221). A regression model has been established by using LSM/OLS method using the
variables stabilized above. As the probability value of the model is 0,0000< 0,05, the model is
significant and the correlation coefficient of the model R2 is 28,12%. When the probability
values of the variables in the model are considered, Moody’s (-1) is the only variable that has
a value less than 0,05. The correlation between the dependent variable CDS (-1) and the
Moody’s (-1) variable, which is significant, can be said to have a relationship with a
coefficient of -17,16162. In other words, a 1-unit increase in Moody’s (-1) leads to a decrease
of -17,16162 in CDS. However, this model must provide some assumptions to be able to say
these results as certain. Alternative methods will be applied if no assumptions are provided.
37
Table 5. The Regression with Least Squares Method
Model
Results
Variables Coefficients
Probability
Values
FITCH (-1) -0,835235 0,8691
Moody’s (-1) -17,16162 0,0003
S&P (-1) -7,174311 0,0589
C -1,165716 0,8017
R2=28,12
5.1.5. The Assumptions
5.1.5.1. The Normality Assumption
One of the assumptions made by the LSM/OLS and needed to be provided in most
regression models is the assumption of normality. In the Graph 1, the probability value of
regression model was found as 0,0000. Since this probability value is less than 0.05, the
hypothesis of “ : Data in the model is normally distributed” is rejected. The use of this
model is not suitable as it does not show a normal distribution.
Graph 1. The Graph of Normality Assumption
5.1.5.2.The Analysis of Outliers
The fact that using the LSM/OLS would not yield healthy results was seen in the
normalization assumption study above. This assumption is not sufficient. In addition, an
outlier analysis was also carried out. The outlier values are values that cause some
irregularities in the model structure and distribution found in the tail parts of the model chart.
There are many methods for determining these values. In this study, RStudent and DFFITS
methods were used. As seen in Graph2 and Graph 3, there are outliers that go beyond the
confidence limits. Therefore, the assumption that there is no outlier value is not provided and
the study will be continued with the alternative method, that is Quantile Regression.
Graph 2. RStudent Method
38
Graph 3. DFFITS Method
5.1.6. Quantile Regression
Quantile Regression is a type of regression used when one or more of the regression
assumptions are not provided. The normality assumptions are violated in this method. There is
no need for absence of outliers or homogeneity. The quantile regression was preferred
because of the extreme values seen in the model made by LS method. If the researcher is
interested in the average method, then the LS method is suitable, while it is more appropriate
to use Quantile Regression if he/she is interested in the median. Quantile Regression can also
be expressed as a settlement model. The Simple Placement Model is expressed by the
following formula:
=ß+ (3)
here is an independent, ß median random variable with symmetric F distribution
function (Saçaklı, 2005).
In this method, the variables in Quantile Regression were examined with 0,25, 0,50 and
0,75 quantiles. The results of each model installed for these quantiles were given in the tables
below. A model is created by separating the lowest 25% of the data part from the highest 75%
of the data (the left tail portion of the distribution) in the 0,25 quantile and the interpretations
are made according to this section. The 0,50 quantile is also called as the expected value or
39
2nd
quarter. In this model, the data set is halved and examined. Finally, in the 0,75 quantile,
25% of the highest data in the data set is examined separately from the remaining 75% (right
portion of the distribution) and the interpretations are made according to this section. In
Quantile Regression, the data is examined part by part because the tail parts are important in
the distribution of the data.
In Table 6, if the CDS is a dependent variable, then different quantile models are
formed with the other variables. As the probability values of all variables are greater than
0.05, the model is meaningless. Moreover, the coefficients are not of any importance. The
constant value of c was found to be significant in 0,25 and 0,75 quantiles. Since the
probability values of these three models are larger than 0,05 as in Table 6, then these three
models are meaningless. As a result, it is said that Fitch, Moody’s and S & P variables have
no effect on CDS variable and so CDS is not affected by increase or decrease of these
variables.
Table 6. The Results of Quantile Regression
Quantile Values 0,25 0,50 0,75
Variables Coefficients Probability
Values
Coefficients Probability
Values
Coefficients Probability
Values
FITCH (-1) -0,345030 0,9767 -2,907078 0,4575 -0,453313 0,8800
Moody’s (-1) -10,80843 0,1721 -4,274398 0,5807 -2,879518 0,5616
S&P (-1) -7,743072 0,1275 -4,476054 0,3646 -2,022289 0,4385
C -19,66500 0,0020 2,028000 0,6918 18,32100 0,0001
Table 7. The Probability Values of Quantile Regression Models
Models 0,25 quantile 0,50 quantile 0,75 quantile
Probability Values 0,4696 0,5108 0,2280
6. CONCLUSION:
In conclusion, the application results show that Fitch, Moody’s and S & P variables
have no effect on CDS variable and so CDS is not affected by increase or decrease of
these variables. This may be due to the fact that credit rating agencies have announced
their rating on certain dates, and that the most recent rating value is currently taken for
comparisons with monthly CDS data. The result obtained is compatible with the following
comment as Ismailescu & Kazemi (2010) stated; “For the emerging economies at the
sovereign level, the positive rating announcements are found to have significant impact on
CDS spreads while the negative rating announcements are found to have no impact”.
The reason why R2 is 28,12% in the OLS application and only Moody’s is included in
the model is that there is 90-95% relationship between the ratings of the three rating
agencies. In other words, when one of these three explanatory variables is taken into the
model, the other two are not needed. There are also two reasons why R2 is low in the
model; the first is that only one explanatory variable in the model, and the second is the
relationship between CDS and rating agencies is low. This is because while CDS values
change from moment to moment according to financial risk, ratings of the countries are
40
not only effected by financial variability but also depend on social-political states, the
progress or regression of democracy, war situations within country or neighbours; that is
rating process considers the situation in a broad perspective. Therefore, the QR results
were not as different as expected.
41
7. REFERENCES:
Alma, Ö. G., Vupa, Ö. (2008). Regresyon Analizinde Kullanılan En Küçük Kareler ve En
Küçük Medyan Kareler Yöntemlerinin Karşılaştırılması. SDÜ Fen Edebiyat Fakültesi Fen
Dergisi, 3 (2) s.219-229.
Arbia, G. (2006). Spatial Econometrics: Statistical Foundation Application to Regional
Convergence. Springer, Berlin.
Aydın, H. (2018). Kredi Derecelendirme Kuruluşları Türkiye Bankalar Birliği Yönetim
Kurulu Başkanı İstanbul Ticaret Üniversitesi.
Chaplin, G. (2005). Credit Derivaties, Risk Management, Trading and Investing, John Wiley
and Sons,Ltd, West Sussex.
Chen, C., Wei, Y. (2005). Computational Issues for Quantile Regression, Special Issue on
Quantile Regression and Related Methods. 67(2), pp.399-417.
Crouhy, M., Galai, D., and Mark, R. (2001). Prototype risk rating system. Journal of Banking
& Finance, 25(1), pp.47-95.
Fabozzi, F.J. (2001). Handbook of Fixed Income Securities, 6th Edition, McGraw-Hill
Publishers, New York.
Ferra, Y., Hazmira Y., and Izzati, R. (2016). Penerapan Metode Regresi Kuantil Pada Kasus
Pelanggaran Asumsi Kenormalan Sisaan. Eksakta, 1 (17), pp.33-37.
Feng, X., Zhu, L. (2016). Estimation and Testing of Varying Coefficients in Quantile
Regression. Journal of The American Statistical Association 111, pp.266-274.
Furno, M. ve Vistocco, D. (2018). Quantile Regression: Estimation and Simulation. Hoboken,
John Wiley & Sons Ltd.
Galil K., Shapir O.M. , Amiram D., and Ben-Zion U. The determinants of CDS spreads.
Journal of Banking & Finance, 41 (2014), pp. 271-282.
Gujarati D.N., Porter D.C. (2005). Essentials of Econometrics (Book), p.718.
Hui, C. H., Fong, T. P. W. (2015). Price cointegration between sovereign CDS and currency
option markets in the financial crises of 2007e2013. International Review of Economics &
Finance, 40, 174e190.
Hull, J.C., White, A. (2000). Valuing credit default swaps I: No counterparty default risk.
Journal of Derivatives, vol.8, no.1, pp. 29-40.
Ismailescu, I., Kazemi, H. (2010). The reaction of emerging market credit default swap
spreads to sovereign credit rating changes. Journal of Banking & Finance 34, pp. 2861–
2873.
Koenker, R., Bassett, G. Jr. (1978). Quantiles Regression: Econometrica. Journal of the
Econometric Society, 46, pp. 33-50.
Koenker, R., Hallock, K. F. (2001). Journal of Economic Perspectives, 15 (4), pp.143–156.
42
Kurtoğlu, F. (2001). Quantile Regresyon: Teorisi ve Uygulamaları. Çukurova Üniversitesi
Fen Bilimleri Enstitüsü İstatistik Anabilim Dalı, Yüksek Lisans Tezi, 15.
Levy, A. (2009). Essays on credit default swaps. Ph.D. Diss., University of California.
Micu, M., Remolona, E. M., and Wooldridge, P. (2004, June). The price impact of rating
announcements: evidence from the credit default swap market. Retrieved December 30,
2013, from http://www.bis.org/publ/qtrpdf/r_qt0406e.pdf.
Mengle, D. (2007). ‘Credit derivatives: An overview, economic review’, Federal Reserve
Bank of Atlanta Working paper, fourth quarter 2007.
Poon, P. H., Chan, K. (2010, August 24). ADBI Working Paper No. 244. Retrieved May 19,
2014, from Social Science Research Network:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1671452.
Saçaklı, İ. (2005). “Kantil Regresyon ve Alternatif Regresyon Modelleri ile Karşılaştırılması”,
Marmara Üniversitesi Sosyal Bilimler Enstitüsü Ekonometri Anabilim Dalı, Yüksek Lisans
Tezi, s.80-81.
Sjö B. (2008). Testing for Unit Roots and Cointegration, pp.1-26.White, L. (2010). Markets:
The credit rating agencies. Journal of Economic Perspectives 24 (2), pp. 221-226.
Yang L., Morley B., Hudson, J. (2010). A study of the causal relationships between sovereign
CDS spreads, risk-free interest rates and exchange rates 8th INFINITI conference on
international finance, 14–15 May, Dublin.
Yıldırım, H.H., Yıldız C., and Aydemir, Ö. (2018). Kredi Derecelendirme Kuruluşlarından
S&P, Moody’s ve Fitch’in Türkiye için Yapmış Oldukları Not Açıklamalarının Hisse
Senedi Endeksleri Üzerine Etkisi: Borsa İstanbul Örneği 2012-2016*, Maliye ve Finans
Yazıları - 2018 - (109), pp. 9-30.
Web Site:
https://www.mathsisfun.com/data/correlation.html. Accessed in April.2019.
![Bedri Noyan (Dede baba) - Veli Baba Menakıbnamesi [Can-1993].pdf](https://img.dokumen.tips/doc/110x75/563dbb9a550346aa9aae9ed8/bedri-noyan-dede-baba-veli-baba-menakibnamesi-can-1993pdf.jpg)
