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DECLARATION
I hereby declare that the dissertation entitled Price Integration in the IndianStock Market: BSE Sensex and S&P CNX Niftyis theresultofworkundertaken by me, under the guidance and supervision of Dr.T.V.N.Rao, Associate
Professor, M.P.Birla Institute of Management,Bangalore.
Ialsodeclare that thisdissertationhas notbeen submitted
to any other University/Institution for the award of any Degree
or Diploma.
Place:Bangalore
Date: 16th
June2006 Chiranjeevi Samudrala
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Principal Certificate.
I hereby certify that the research work embodied in
this dissertation entitled Price Integration in the IndianStock Market: BSE Sensex and S&P CNX Niftyhas been
undertaken and completed by Mr.Chiranjeevi Samudrala underthe guidance and supervision ofDr.T.V.N.Rao, Faculty, MPBIM,
Bangalore.
Place:Bangalore Dr.N.S. Malavalli
Date:16/06/2006 PrincipalMPBIM, Bangalore
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Guide Certificate.
I hereby declare that the research work embodied in
this dissertation entitled Price Integration in the IndianStock Market: BSE Sensex and S&P CNX Niftyhas been
undertaken and completed by Mr.Chiranjeevi Samudrala undermy guidance and supervision.
Place:Bangalore (Dr.T.V.N.Rao)
Date: 16/06/2006 Faculty Member.
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ACKNOWLEDGEMENT
I take this opportunity to sincerely thank Dr.T.V.N Rao
who guided me through out the project through his
valuable suggestions, without which the project would
not have been successful.
I also thank Dr N.S. Malavalli (Principal) for giving me
the opportunity to explore my areas of interest by consistently
lending support in terms of his expertise and also supplying valuable
inputs in terms of resources every step of the way.
My sincere thanks to my parents and friends who out of
hard sweat were able to help me at all time and given
encouragement for successful completion of this project.
Chiranjeevi Samudrala
(04XQCM6020)
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Serial no CONTENTS Page no
Executive Summary
Introduction 1
a).National Stock Exchange 1
b).Bombay Stock Exchange 3
Chapter 1
c). The structure of Indian Capital market and need for the study 4
Chapter 2 Review of Literature 7
Methodology 14
3.1 Research Problem 14
3.2 Objectives of the Study 14
3.3 Hypothesis of the Study 14
3.4 Limitations of the Study 14
3.4 Study Type 15
3.5 Study Population 15
3.6 Sample 15
3.7 Sampling Technique 15
3.8 Period of Study 15
Chapter 3
3.9 Data Gathering 15
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3.10 Statistical Models 16
Data Analysis and Interpretations
Table 1: Unit Root Test for BSE Daily and Interpretation 21
Table 2: Unit Root Test for BSE Monthly and Interpretation 22
Table 3: Unit Root Test for NSE Daily and Interpretation 23
Table 4: Unit Root Test for NSE Daily and Interpretation 24
Table 5: Grangers Cointegration Test for BSE and NSE
Daily and Interpretation for X on Y
25
Table 6: ANOVA for BSE and NSE Daily and Interpretation for
X on Y
26
Table 7: Grangers Cointegration Test for BSE and NSE
Daily and Interpretation for Y on X
27
Table 8: ANOVA for BSE and NSE Daily and Interpretation for
Y on X
28
Table 9: Grangers Cointegration Test for BSE and NSE
Monthly and Interpretation for X on Y
29
Table 10: ANOVA for BSE and NSE Monthly and
Interpretation for X on Y
30
Table 11: Grangers Cointegration Test for BSE and NSE
Monthly and Interpretation for Y on X
31
Chapter 4
Table 12: ANOVA for BSE and NSE Monthly and
Interpretation for Y on X
32
Chapter 5 Conclusions 33
Chapter 6 Annexure 34
Chapter 7 Bibliography
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EXECUTIVE SUMMARY
There are various studies, which have analyzed the co-moments and cointegration
between various stock exchanges of different countries. We are not sure whether the
fluctuations of one index will affect the other and whether they are cointegrated or not.
The objective of the study is to examine the price integraton between two stock price
indices BSE sensex and S&P CNX Nifty in India from January 2000 to January 2006.
The performance and development of both the stock exchanges over the period has been
revealed every year.
In this we first tested whether the time series is stationary or not. For this AugmentedDickey fuller unit root test at different lags such as lag 0 and at lag 12. After examining
the series is stationary or not Engel-Granger test is conducted to test whether the Bombay
Stock Exchange and National Stock Exchange at different lags and found that there is
sufficient evidence for price integration between both the stocks.
The findings of the study are for daily and monthly closing BSE and Nifty are
cointegrated at different lags.
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INTRODUCTION:-
Integration is a process by which markets become open and unified so that, participants
in one market have an unimpeded access to other markets. The financial market's
integration in general implies that in the absence of administrative and informational
barriers, risk adjusted returns on assets of the same tenor in each segment of the market
should be comparable to one another. The empirical investigations of market integration
between two markets could be examined through various statistical and econometrics
techniques. Correlation analysis is a suitable technique, which has been widely and
extensively used in past for examining market integration. The prices of various assets in
these markets were the principal instrument and barometer. If the estimated correlation
coefficient is close to plus or minus one, then the prices between the markets was
considered as the supporting evidence for market integration. However, correlation
analysis has its own limitations. It suffers from the important limitation of possible serial
correlation, thus provides spurious or not meaningful results. In order to analyze the co-
movements of international stock prices and thereby stock market integration, most of the
studies applied cointegration techniques. The study applies the Engel-Engel-Granger
cointegration technique which is a popular and suitable technique for two variables.
NATIONAL STOCK EXCHANGE (NSE)
With the liberalization of the Indian economy, it was found inevitable to lift the Indian
stock market trading system on par with the international standards. On the basis of the
recommendations of high powered Pherwani Committee, the National Stock Exchange
was incorporated in 1992 by Industrial Development Bank of India, Industrial Credit and
Investment Corporation of India, Industrial Finance Corporation of India, all Insurance
Corporations, selected commercial banks and others.
Trading at NSE can be classified under two broad categories:
(a) Wholesale debt market and
(b) Capital market.
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Wholesale debt market operations are similar to money market operations - institutions
and corporate bodies enter into high value transactions in financial instruments such as
government securities, treasury bills, public sector unit bonds, commercial paper,
certificate of deposit, etc.
There are two kinds of players in NSE:
(a) Trading members and
(b) Participants.
Recognized members of NSE are called trading members who trade on behalf of
themselves and their clients. Participants include trading members and large players like
banks who take direct settlement responsibility.
Trading at NSE takes place through a fully automated screen-based trading mechanism
which adopts the principle of an order-driven market. Trading members can stay at their
offices and execute the trading, since they are linked through a communication network.
The prices at which the buyer and seller are willing to transact will appear on the screen.
When the prices match the transaction will be completed and a confirmation slip will be
printed at the office of the trading member.
NSE has several advantages over the traditional trading exchanges. They are as follows:
NSE brings an integrated stock market trading network across the nation.
Investors can trade at the same price from anywhere in the country since inter-market
operations are streamlined coupled with the countrywide access to the securities.
Delays in communication, late payments and the malpractices prevailing in the
traditional trading mechanism can be done away with greater operational efficiency and
informational transparency in the stock market operations, with the support of total
computerized network.
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BOMBAY STOCK EXCHANGE:
Bombay Stock Exchange Limited is the oldest stock exchange in Asia with a rich
heritage. Popularly known as "BSE", it was established as "The Native Share & Stock
Brokers Association" in 1875. It is the first stock exchange in the country to obtain
permanent recognition in 1956 from the Government of India under the Securities
Contracts (Regulation) Act, 1956.The Exchange's pivotal and pre-eminent role in the
development of the Indian capital market is widely recognized and its index, SENSEX, is
tracked worldwide. Earlier an Association of Persons (AOP), the Exchange is now a
demutualised and corporatised entity incorporated under the provisions of the Companies
Act, 1956, pursuant to the BSE (Corporatisation and Demutualisation) Scheme, 2005
notified by the Securities and Exchange Board of India (SEBI).
With demutualisation, the trading rights and ownership rights have been de-linked
effectively addressing concerns regarding perceived and real conflicts of interest. The
Exchange is professionally managed under the overall direction of the Board of
Directors. The Board comprises eminent professionals, representatives of Trading
Members and the Managing Director of the Exchange. The Board is inclusive and is
designed to benefit from the participation of market intermediaries.
The Exchange has a nation-wide reach with a presence in 417 cities and towns of India.
The systems and processes of the Exchange are designed to safeguard market integrity
and enhance transparency in operations. During the year 2004-2005, the trading volumes
on the Exchange showed robust growth.
The Exchange provides an efficient and transparent market for trading in equity, debt
instruments and derivatives. The BSE's On Line Trading System (BOLT) is a proprietory
system of the Exchange and is BS 7799-2-2002 certified.
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The Structure of Indian Capital Market and need for the study
The Indian financial system has undergone a sea change over the years especially after
nineties. Until the early nineties, it was characterized by regulated and administered
regime. The interest rates were administered, various markets participantsincluding
banks, financial institutions and corporate were restricted in terms of the nature and
volume of transactions they could undertake in various financial markets including the
money, for-ex and capital markets. The administrative limits were also imposed on the
transactions between residents and non-residents. However, a drastic change occurred
since mid-1991, when RBI has taken several steps to develop various segments of the
financial markets, strengthen their integration and enhance their efficiency, covering
various markets including stock market Financial system has become market oriented
rather than strictly controlled.
The structure of Indian capital market, consisting of primary and secondary market, has
evolved over time. The raising of resources in the primary market was subject to several
controls and restrictions until the onset of economic reforms of early nineties. The pricing
to be determined by market forces was disallowed. The secondary market transactions
were impenetrable. The trading and settlements system was traditional, old and almostoutdated. Informational flows to the markets participants were also inefficient. In spite of
these the volume of trading has marked substantial increase. An important development
in this respect is the statutory power given to Securities and Exchange Board of India
(SEBI) to undertake regulatory and supervision of capital market. Since then the
developmental process of capital market began. The introduction of SEBI guidelines is an
important hallmark to protect investors interest and promoting development of primary
market. One example of the developmental process is the introduction of book building
mechanism, which provides issuer the choice to raise resources either through IPOs
(Initial public Offerings) or fixed price mechanism. Both NSE and BSE offer their
infrastructure for conducting online IPOs through such book building. Online trading
system and Over The Counter (OTC) were also introduced to make the trading system
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easy and transparent. This could provide a sound background to establish the strong
relationship between the stock markets.
The capital market has also widen and deepened considerably in the recent years with the
enlargement of participants and emergence of new instruments in both markets. Besides
equity and debt instruments various derivatives instruments were allowed for trading. The
mutual funds and foreign institutional investors were also allowed to participate in the
stock markets. The trading, clearing and settlement systems have also been considerably
improved. The introduction of rolling settlement system shortens the settlement cycle.
These changing capital structures have significant positive impact on volatility, liquidity
and transaction costs over the years. Though the stock market continues to be volatile, the
volatility tended to be declined in recent years. The growth of liquidity measured by
traded value ratio and turnover ratio suggest that liquidity has increased in recent years.
However, despite the growing popularity of stock markets during 80s and 90s the
transaction costs are high maybe due to physical moment of paper, bad deliveries etc.
The reforms in Indian stock market started since mid-90s. As a part of the reform process
the two major stock exchanges viz., Bombay Stock Exchange (BSE). And National Stock
Exchange (NSE) has expanded their operations in different locations. Thus, they provide
investors across the country with the facility to trade in the stock listed/permitted in these
stock exchanges. Though various stock exchanges continued to follow different system of
settlement procedure, certain developments have resulted in better performance in the
various segments of the Indian securities markets. The Interconnected Stock Exchange of
India Ltd. (ICSI) has been set up as an interconnected market system. It provides its
trading members the facility to trade on the national market in addition to the trading
facility at the regional stock exchange. This has integrated various regional stock
exchanges although trading activity in the ICSI has not been very significant. Many
regional stock exchanges have also become members of the BSE and NSE, which further
strengthen the integration process of various stock exchanges in the country. With the
development of various trading techniques, the information from one market to the other
passes quickly, so also the stock price, returns and volatility.
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The performance and development of both the stock exchanges over the period can be
revealed from the data itself, which could also provide some useful information about
their relationship. The total market capitalization, daily turnover and total turnover at
NSE in November 1994 was Rs. 292637 cr, Rs. 7 cr and Rs. 125 cr respectively, which
has increased to Rs. 1585585 cr, Rs. 5139 cr and Rs. 113055 cr in March 2005. Where as
at BSE it was Rs. 401692 cr, Rs. 442 cr and Rs. 8831 cr during November 1994, and has
increased to Rs. 1698428, Rs. 2706, and Rs. 59512 cr in March 2005 respectively. The
number of listed companies in January 1996 and March 2005 at NSE was 406 and 970,
whereas at BSE it was 5451 and 4731(declines since June 2004) respectively. The total
returns of S&P CNX Nifty during 1994-95 was 15.88% and has increased to 14.89%, in
2004-05, whereas for BSE Sensex it was 13.71% and 16.14% respectively. On the other
hand the volatility of S&P CNX Nifty during 1994-95 and 2004-2005 was 1.13% and
1.61%, whereas for BSE Sensex it was 1.17% and 1.48% respectively. The average
number of sharers traded daily at NSE has increased from 43031681 in April 1996 to
380337290 in March 2005. Similarly, average number of sharers traded daily at BSE has
increased from 35162357 in April 1996 to 275609732 in March 2005. If we look at the
average value of trading daily, it shows increasing pattern both at NSE and BSE. At NSE
it has increased from Rs. 864 cr in April 1996 to Rs. 5137 cr in March 2005, similarly, at
BSE this is Rs. 368 and Rs. 2642 cr. It shows that both markets are simultaneously
developing and hence, follow some equilibrium relationship. In these contexts it is felt
necessary to examine the price integration between the two stock markets and see
whether they are related or not.
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LITERATURE REVIEW:
The purpose of literature review is to find out the various studies that have been
done in the relative fields of the present study and also to understand the various
methodologies followed by the authors to arrive at the conclusions.
The following are some of the relevant studies
According to Mahesh Kumar Tambi attempts to examine the financial integration of
emerging or newly industrialized countries and developed economies and test it
empirically. Stock market data have been used for the purpose of the study. Paper
considers three developed countries: USA, CANADA & UK and three developing
nations: India , Malaysia , Singapore.
The paper mainly discuss the degree of integration of Indian Stock market with other
developing and developed natins stock markets using various techniques like Engle
Engel-Granger two stage method, Johansen cointegration method, VAR-ECM , principle
Component Analysis and Impulse-response analysis.
Fianancial market integration can be understood as a situation where there are no
quantitative and qualitative barriers like tariffs,taxes,restriction on trading in foreignassets or information costs with hampers the free flow of capital from one market to
another. Fianancial market integration is a buzzword now a day. Fianancial markets can
be considered integrated if there is no barier on free capital mobility and same risk assets
command the same return across the different markets.
The paper uses the daily sock index data for a period of 11 years for three developing and
three developed countries US, Canada, UK, India, Singapore and Malaysia. Most popular
indexes of respective countries are selected for study like S&P/TSX Composite Index for
Canada, S&P 500 index for US , BSE sensex for India, Straits Time Index for Singapore,
FTSE 100 Index for UK and Composite Index for Malaysia. In this four stage approach.
In the First stage integration of the series was tested using the unit root hypothesis on the
logarithms of the indices.
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The testing procedure followed is Dickey Fuller and augmented Dickey Fuller(ADF) as
well as respective tests incorporating a deterministic trend. In the second stage a
multivariate VAR system is constructed, with its corresponding VECM. Then maximum
likelihood tests of Johansen(1988) and Johansen and Jusilius are used to determine the
number of cointegrating vectors. The third stage used Engel-Granger causality through
the analysis of a vector error correction feedback mechanism in cointegrated models .
block Engel-Granger non-casuality, which is a variation of the Engel-Granger causality
restricted model that tests for mutual depentdency on each of the other variables lag
structures, is applied to the non-cointegrating VAR models. The last stage follows the
autoregressive distributed lag (ARDL) approach to cointegration, developed by Peasaran
and Shin (1995) based on the results of the previous two sections.
The tests show that India is cointegrated with both developing economies like US,UK
and Canada and other developing economies like Malaysia and Singapore. Canada being
a closed economy shows no cointegration with other countries. UK and USA are
cointegrated with each other. The economies Malaysia and Singapore are open to each
other and show a high level of integration with each otherl. The tests also shows some
contradictory results like India is integrated with all other six countries considered in the
test when India is taken as the dependent variable but when the regression was run taking
India as independent variable and residuals were tested for stationary it was observed that
India was not integrated with the countries.
According to Bala Arsanapalli, he examined the linkages and dynamic interaction among
stock price indices in the major world stock exchanges. The data used in this study are
daily closing stock market index time series.
This study concentrates on the worlds 5 largest stock exchanges : New York , Frankfurt
,London , Japan and Paris. The stock price performance across exchanges for the month
of October 1987 is characterized as very unusual in the rectent history of the stock
market. To assure that the results are not being influenced by the stock price data of this
period, two additional data sets are employed in this study: the pre-crash (January 1980-
September 1987) and the post-crash (November 1987 May 1990). Since national stock
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markets are generally operating in different time zones with different opening an closing
times, it is important to note that there is no trading overlap between the Tokyo stock
exchange and the exhanges in Paris , Frankfurt and London and between the New York
stock exchange and the exchanges in Frankfurt , paris and finally between the New York
and Tokyo exchanges.
In his research he uses a cointegration test which involves four steps.
Determine the presence of units(order of integration) by using Dickey Fuller and
Augmented Dickey Fuller
The second state involves estimating the following co integration regression
Xt = Ct + dyt, + zt
Where Xt = US stock market Index
yt = foreign stock market Index
In co integration the null hypothesis is non-co integration
We test for the stationarity of the co integration regression equation in error (zt )
DZt = -PZ t_ 1 +et
4. The estimation of error-correction model
Xt - Xt-1 = a0 + a1 Z t_ 1 +B1 (L) (Xt - Xt Xt ) + B2 (L)( yt - yt-1 ) + et
The evidence indicates that the degree of integrational comovements in stock price
indices has changed significantly since the crash of October 1987, with the Nikkei index
the only exception. Specifically, for the pre-crash period he find that France , germany
and UK stock markets are not related to the US stock market. This result is not consistent
with previous studies, which report substantial interdependence among these stock
markets. For the post-crash period, however , our results show that the major European
stock markets are indeed strongly linked with the US stock market. Moreover, the error-
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correction analysis given results with respect to the stock market interactions among the
five major world stock exchanges. The US stock market is found to have a substantial
impact on the French, German and UK markets in the post-crash period. Stock market
innovations in any of the three European stock markets have no impact on the US stock
market. In addition, he found no evidence of interdependence among the stock price
indices between US and Japan. He also found that the US and japan stock markets have
drifted far away from each other since the October crash. Finally a similar result is
obtained between japan and the three European stock markets. The pattern of
interanctions among France, Germany, UK and Japan suggests that Japanese stock
market innovations are unrelated to the performance of the major European stock
markets.
According to Bala Arsanapalli he examined the common stochastic trends among
national stock prices of the U.S. and five East Asian countis, including Japan, Taiwan,
Hong Kong, Singapme, and South Korea.
The methodology he used is JOHANSENS PROCEDURE.
JOHANSENS PROCEDURE
Xt = + xt-1 c . . . + t -1 Xt-k +t
Where: - Xt and , are of dimension p x 1, , - N(O,A), and Qs are p x p and p x 1
Regression coefficients. Following Johansen (1988, 1991), and Johansen and Juselius
(1990), Equation 1 can be reparametrized as:
Xt= + xt-1 +. . . + t -1 Xt-k+1 + xt-k
The short-term dynamics of the model are captured by matrices I, through Fk_1, while
matrix II provides information about the long-run relationships among the series. If the
series are nonststionary but co integrated, the rank of II, denoted by r, is less than the
dimension of II (i.e., 0 < r< p), and equals the number of co integration vectors in the
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system. In this case, there exist r stationary cointegrating relationships among the series
and p r common unit roots dictating the long-run stochastic trend of the variables.
He founded that the stock price series are found to be nonstationary and yet co integrated.
Two co integrating relationships are identified and the six stock price variables are found
to share four common unit roots. The result shows that the stochastic trends dictated by
the four common unit roots are important to the long-run movement of the stock prices,
especially those of the U.S. and Taiwan. Though not conclusive, the result suggests that
U.S. and Taiwan markets may not belong to a common stock region containing the
remaining four countries. The result also shows that most variables have the same
adjustment speed in moving from short-run disequilibria toward the common trend.
There are some more authors who studied different market to know whether they are
cointegrated or not. Hordick (1972), Argy and Hodreja (1973) and Salant and Sweeny
(1976) tested the degree of integration in different markets using different techniques.
Fase (1976) found evidence of substantial degree of market integration in eleven
European countries, base on monthly short-term interest rate data for the period of 1961-
1972 and using Principle Component analysis technique. The wave of globalization
accompanied by financial sector reforms in many emerging countries during 1990s (or
1980s more specifically) motivated many empirical studies in this area.
Mishkin (1982) studied the equality of real interest rates and other parity conditions for
countries UK, West Germany, Netherlands and Switzerland and found evidences that real
interest rates are not equal in these countries, although he acknowledged that there is a
tendency for real interest rates across these countries are equalizing over time.
Mark (1983), Cumby and Mishkin (1984) investigated the movement of real interest rates
in developed countries and found a strong positive correlation between interest rate
movements in US and these countries. Kasa (1992) examined number of common
stochastic trends in the equity market of US, Japan, England, Germany and Canada and
found a strong common trend driving stock prices of these countries
Cheun and Mark (1992) using weekly return series for the period of 1977 and 1988
Investigated the relationship between the two developed markets US and Japan and eight
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Asian-Pacific markets; Australia, HK, Korea, Malaysia, Philippines, Singapore, Taiwan
and Thailand and found that US market leads the stock market of most of these countries
with the exception of Korea, Taiwan and Thailand. While Japanese market found to have
a less important influence in this region. Malliaris and Urrutia (1992) analyzed lead-lag
relationship for six major stock market indexes2 for before and after 1987 market crash.
Although they did not find any causality for pre-crash and post-crash period but they
found important feedback relationship and unidirectional causality for the month of
causality.
Chung and Liu (1994) conducted a study to examine the common stochastic trend among
national stock prices of the US and five East Asian countries Japan, HK, Singapore,
Taiwan and Korea. Their study suggests that except Taiwan, all other countries in the
sample has a strong linkage with US market and holds same speed of adjustments from
short term disequilibrium.
Corhay et al (1995) conducted a study to investigate long-run relationship among five
major European markets France, Germany, Italy, Netherlands and UK and found
evidences of strong integration among these countries. Korajczyk (1996) and Harvey
(1995) found asymmetric integration relationship; stock markets of developed notions are
more integrated than those of emerging nations.
Choudhary (1994) test the stochastic structure of individual stock markets of US, UK,
Japan, Italy, France, Canada and Germany. Their study supports the efficient market
hypothesis. All stock indices contain a long-term permanent stochastic trend (unit root)
that makes long run predictions impossible. Using Johansen method of cointegration,
they found no evidence of the presence of common stochastic trend among these stock
markets (for the period of 1953-1989). In a different paper, same author (Choudhary
1997) used a bivariate framework for the period of 1985-1993 for six Latin-American
markets and found support for the existence of long-run relations
Solnik et al (1996) examined the correlation of volatility in stock prices in different
markets and found that this correlation increases during the period of high market
volatility. They also found that in the last 37 years (1959-1995) correlation of individual
foreign markets with the US stock market has increased slightly, but in the last 10 yrs
(1985-1995) there is no significant increase in this correlation.
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Research problem
There are various studies, which have analyzed the co-moments and
cointegration between various stock exchanges of different countries. We are not sure
whether the fluctuations of one index will affect the other and whether they are
cointegrated or not. This study examines the price integraton between two stock price
indices BSE sensex and S&P CNX Nifty in India.
Objectives of the study
To examine the price integration between the two domestic stock markets in India
i.e., Bombay Stock Exchange and National Stock Exchange, using the daily and monthly
closing on BSE Sensex and S&P CNX Nifty, from January 2000 to January 2006. Using
cointegration techniques of Engel- Engel-Granger at different lags the study finds that
there is sufficient evidence of long run relationship between the prices of both the
markets
Hypothesis of the study
Hypothesis 1
H0: There is no significant relation between BSE Sensex and S&P CNX Nifty.
H1: There is significant relation between BSE Sensex and S&P CNX Nifty.
Limitations of the study
The primary focus of the study is on the co movements between BSE Sensex and
S&P CNX Nifty by using Engle-Engel-Granger technique only.
The study is limited to only for two stock exchanges in India.
This study is limited for the period of January 2000 to January 2006
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Study Type: The study type is analytical, quantitative and historical.
Analytical because facts and existing information is used for the analysis,
Quantitative as relationship is examined by expressing variables in
measurable terms
Historical as the historical information is used for analysis and interpretation.
Study population: population is the closing of national stock exchange & Bombay
stock exchange.
Sample: Sample chosen is daily and monthly closing values of BSE Sensex, S&P CNX
Nifty.
Sampling technique: Deliberate sampling is used because only particular units are
selected from the sampling frame. Such a selection is undertaken as these units represent
the population in a better way and reflect better relationship with the other variable.
Period of the study: the period is different for different indices. S&P CNX nifty is
taken for ten years from January , 2000 to January , 2005, and BSE Sensex from January
, 2000 to January , 2005.
Data gathering procedures and instruments:
Data: Historical values of monthly closing and daily closing of BSE Sensex and S&P
CNX nifty.
Data Source: Historical share prices of the NSE sample are taken from
www.nseindia.com and BSE from www.financeyahoo.com .
Statistical Models
Augmented Dicky Fuller test to test the stationary of the series.
Engel-Grangers cointegration approach to test for co integration between the series.
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Statistical Models
In this study, a co-integration approach the Engle-Engel-Granger methodology is
applied to study whether the BSE Sensex, S&P CNX Nifty are cointegrated before doing
co-integration analysis, it is necessary to test whether the time series are stationary at
levels by running Augmented Dickey fuller (ADF) test on the series. Because most time
series are non stationary in levels, and the original data need to be transformed to obtain
stationary series
Stationarity
According to Engle and Engel-Granger, a time series is said to be stationary if
displacement over time does not alter the characteristics of a series in a sense that
probability distribution remains constant over time. In other words, the mean, variance
and co-variance of the series should be constant over time. A nonstatioanry time series
will have a time varying mean or a time varying variance or both or are
autocorrelated.The degree of co-integration is closely related with stationary.
It is evident from the time-series literature that the standard estimation and
statistical test procedures are highly inappropriate, and even invalid, when the variables
involved are nonstationary.
The empirical works based on time series data assumes that the underlying time
series is stationary. In regressing a time series variable on another time series variables,
one often obtains a very high R2 (residuals) even though there is no meaningful
relationship between the two variables. This situation exemplifies the problem of
spurious or nonsense regression, which arises when data is non stationary.
A series is said to be integrated of order one [I (1)] if it has to be differentiated
once before becoming stationary. Similarly, a series is of order two [I(2)] if it has to be
differentiated twice before becoming stationary.
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test is carried out by estimating an equation with Yt-1 subtracted from both sides of the
equation.
yt = C + t-1 + t
Where = (-1), and the null and alternative hypotheses are
Ho: = 0 ..Non Stationary
H1: < 0 ..Stationary
Dickey and fuller simulated the critical values for selected sample sizes. More recently,
Mackinnon (19991) has implemented a much larger set of simulations than those
tabulated by Dickey and Fuller.
Unit root test [Augmented dickey fuller test]
The simple Unit root test is valid only if the series is an AR (1) Process. If the series is
correlated at high order lags, the assumption of white noise disturbances is violated. [In
other words, in DF test,it was assumed that the error term t was uncorrelated. But in
case the error ter mis correlated, Dickey and Fuller have developed a test, knoen as
Augmented Dickey Fuller test]. The ADF controls for higher - order correlation by
adding lagged difference terms of the dependent variable to the right-hand side of the
regression
Yt = C + t-1 + 1 yt-1 + 2 y t-2 + ..+ p y t-p + t
This augmented specification is then tested
H0: = 0 Non Stationary
H1: < 0 Stationary
The unit root test is based on the following three regression forms:
1. Without intercept and trend (random walk) Yt = Yt-1 + t
2. with intercept (random walk with drift) Yt = + Yt-1 +t
3. with intercept and trend( with drift around a stochactic trend) Yt = T + Yt-1 +t
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Where, is the intercept/constant, T is trend, is the slope i.e level of
dependency and integration, is drift parameter i.e.change from Yt to Yt-1 and t is the
error term.
In general, the procedure start with whether the variables X and Y in its level form under
none, intercept and trend and intercept is stationary. If the hypothesis is rejected, then the
series is transformed into first difference of the variable and tested for stationarity. If first
difference series is stationary, this implies that X and Y are I(1).
Engel-Grangers co-integration Test
The fundamental aim of co integration analysis is to detect any common
stochastic trends in the price data and to use these common trends for a dynamic analysis
of correlation in returns. Correlation is based only on return data, but full co integration
analysis is based on the raw prices, rate or yield as well as return data.
According to co integration theory, two variables that are stationary in changes
are co integration if a linear combination of them in levels is stationary. Thus, changes in
the prices are taken for running the test.
Engel-Granger introduced the concept of co-integration when he wrote that two variables
may move together though individually they are non stationary. Co-integration is based
on the long run relationship between variables. The idea arises from considering
equilibrium relationships, where equilibrium is a stationary point characterized by forces
that tend to push the variables back toward equilibrium.
In general, if Yt and Xt are both integrated of order I (d), then any linear combination of
the two series will also be I (d)... That is, the residuals obtained on regressing Yt on Xt
are I (d).
If two or more series are co integrated then even though the series themselves may be non
stationary, they will move closely together over time and their difference will be
stationary. Their long run relationship is the equilibrium to which the system converges
overtime and the disturbance term Et can be construed as the disequilibrium error or the
distance that the system is away from equilibrium at time t.
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Table 1: UNIT ROOT TEST [AUGMENTED DICKEY FULLER TEST] for BSE
DAILY. In this daily closing of BSE Sensex is taken from January 2000 to January 2006.
LAGS ADF VALUES SIGNIFICANCE
(%)
CRITICAL
VALUES
1 -2.5671
5 -1.9396
0 -35.77700
10 -1.6157
1 -2.5671
5 -1.9396
10 -1.6157
12 -10.52569
10 -1.6157
Level of significance graph
Hypothesis:
H0 = ADF > critical values -- not reject hull hypothesis i.e., unit root exists.
H1 = ADF < critical values reject null hypothesis i.e. unit root does not exist.
INTERPRETATION:-
For ADF test statistic at 0 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist.
For ADF test statistic at 12 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist.
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TABLE 2: UNIT ROOT TEST [AUGMENTED DICKEY FULLER TEST] for BSE
MONTHLY. In this monthly closing of BSE Sensex is taken from January 2000 to
January 2006.
LAGS ADF TEST
STATISTIC
SIGNIFICANCE
(%)
CRITICAL
VALUES
1 -2.5958
5 -1.9450
0 -7.8282292
10 -1.6182
1 -2.6026
5 -1.9462
12 -0.987514
10 -1.6187
Level of significance graph
Hypothesis:
H0 = ADF > critical values -- not reject hull hypothesis i.e., unit root exists.
H1 = ADF < critical values reject null hypothesis i.e. unit root does not exist.
INTERPRETATION:-
For ADF test statistic at 0 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist.
For ADF test statistic at 12lags:-
The ADF test statistics at 12 lags indicates that data is not stationary at the significant
level 1%, 5% and at 10% since the critical values are less than the ADF test statistics the
data is not stationary and the unit root exists. Therefore the null hypothesis is accepted.
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Table 3: UNIT ROOT TEST [AUGMENTED DICKEY FULLER TEST] for NSE
DAILY. In this daily closing of NSE S&P is taken from January 2000 to January 2006.
LAGS ADF TEST
STATISTIC
SIGNIFICANCE
(%)
CRITICAL
VALUES
1 -2.5671
5 -1.9396
0 -34.90966
10 -1.6157
1 -2.5671
5 -1.9396
12 -10.39008
10 -1.6157
Level of significance graph
Hypothesis:
H0 = ADF > critical values -- not reject hull hypothesis i.e., unit root exists.
H1 = ADF < critical values reject null hypothesis i.e. unit root does not exist.
INTERPRETATION:-
For ADF test statistic at 0 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist.
For ADF test statistic at 12 lags:-
The ADF test statistics at 12 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist.
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Table 4: UNIT ROOT TEST [AUGMENTED DICKEY FULLER TEST] for NSE
MONTHLY. In this Monthly closing of NSE S&P is taken from January 2000 to
January 2006.
LAGS ADF TEST
STATISTIC
SIGNIFICANCE
(%)
CRITICAL
VALUES
1 -2.5958
5 -1.9452
0 -8.347865
10 -1.6183
1 -2.6040
5 -1.9464
12 -1.160638
10 -1.6188
Level of significance graph
Hypothesis:
H0 = ADF > critical values -- not reject hull hypothesis i.e., unit root exists.
H1 = ADF < critical values reject null hypothesis i.e. unit root does not exist.
INTERPRETATION:-
For ADF test statistic at 0 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root exists.
For ADF test statistic at 12lags:-The ADF test statistics at 12 lags indicates that data is not stationary at the significant
level 1%, 5% and at 10% since the critical values are less than the ADF test statistics the
data is not stationary and the unit root exists. Therefore the null hypothesis is accepted.
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Engel-Grangers Co integration Test:
Cointegration between S&P CNX Nifty DAILY and BSE SENSEX
DAILY
An ordinary least square (OLS) regression is done on the data. First x is regressed on y
then y on x.
X on Y -- Dependent variable(X) is BSE SENSEX daily and Independent variable(Y) is
S&P NIFTY daily.
Y on X -- Dependent variable(X) is S&P NIFTY daily and Independent variable(Y) is
BSE SENSEX daily.
BSE SENSEX t = a + b S&P NIFTY t + e t
S&P NIFTY t = a + b BSE SENSEX t + e t
TABLE 5: ADF UNIT ROOT TEST X ON Y
LAGS CONSTRAINTS ADF
VALUES
SIGNIFICANCE
(%)
CRITICAL
VALUES
1 -2.5671
5 -1.9396
0 FIRST
LEVEL OF
DIFFERENCE
X ON Y -35.92243
10 -1.6157
1 -2.5671
5 -1.9396
12 FIRST
LEVEL OF
DIFFERENCE
X ON Y -10.56207
10 -1.6157
Level of significance graph
Hypothesis:
H0 = ADF > critical values -- not reject hull hypothesis i.e., unit root exists.
H1 = ADF < critical values reject null hypothesis i.e. unit root does not exist.
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INTERPRETATION:-
For ADF test statistic at 0 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist we can say that BSE and NSE are cointegrated.
For ADF test statistic at 12 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist we can say that BSE and NSE are cointegrated.
Regression analysis:-
ANOVA
TABLE 6Model Sum ofSquares
df MeanSquare
F Sig.
1 Regression 2.938E-04 1 2.938E-04 6.717 .010
Residual 6.518E-02 1490 4.374E-05
Total 6.547E-02 1491
Predictors: (Constant), NSEDAILYDependent Variable: BSEDAILY
Coefficients
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Model B Std. Error Beta
1 (Constant) 1.518E-04 .000 .886 .376
NSEDAILY 6.807E-02 .026 .067 2.592 .010
Dependent Variable: BSEDAILY
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General rule of Cointegration:-
The Grangers Cointegration test has been conducted by running the OLS
Regression equations. The residuals have been obtained for BSE & NSE daily from
the estimated equations. Then the Unit Root test has been done to check the
Stationarity of residual series. The ADF calculated statistics shows that there is no
Unit Root. If the residuals do not have Unit Roots, then the series is said to be
Cointedgrated at I (1). Therefore the series is Cointegrated at I (1,0) and I (1,12). It
is bidirectional with reference to ANOVA TABLE 6.
TABLE 7: ADF UNIT ROOT TEST Y ON X
LAGS CONSTRAINTS ADF
VALUES
SIGNIFICANCE
(%)
CRITICAL
VALUES
1 -2.5671
5 -1.9396
0 FIRST
LEVEL OF
DIFFERENCE
Y ON X -35.7891
10 -1.6157
1 -2.5671
5 -1.9396
12 FIRST
LEVEL OF
DIFFERENCE
Y ON X -11.61969
10 -1.6157
Level of significance graph
Hypothesis:
H0 = ADF > critical values -- not reject hull hypothesis i.e., unit root exists.
H1 = ADF < critical values reject null hypothesis i.e. unit root does not exist.
INTERPRETATION:-
For ADF test statistic at 0 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist we can say that BSE and NSE are cointegrated.
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For ADF test statistic at 12 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist we can say that BSE and NSE are cointegrated.
Regression analysis:-ANOVA TABLE 8
Model Sum ofSquares
df MeanSquare
F Sig.
1 Regression 2.846E-04 1 2.846E-04 6.717 .010
Residual 6.313E-02 1490 4.237E-05
Total 6.341E-02 1491
Predictors: (Constant), BSEDAILYDependent Variable: NSEDAILY
Coefficients
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Model B Std. Error Beta
1 (Constant) 1.490E-04 .000 .884 .377
BSEDAILY 6.593E-02 .025 .067 2.592 .010
Dependent Variable: NSEDAILY
General rule of Cointegration:-
The Grangers Cointegration test has been conducted by running the OLS
Regression equations. The residuals have been obtained for BSE & NSE daily from
the estimated equations. Then the Unit Root test has been done to check the
Stationarity of residual series. The ADF calculated statistics shows that there is no
Unit Root. If the residuals do not have Unit Roots, then the series is said to be
Cointedgrated at I (1). Therefore the series is Cointegrated at I (1,0) and I (1,12). It
is bidirectional with reference to ANOVA TABLE 8.
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INTERPRETATION:-
For ADF test statistic at 0 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist we can say that BSE and NSE are cointegrated.
For ADF test statistic at second level of difference 12 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist we can say that BSE and NSE are cointegrated.
Regression analysis:-ANOVA TABLE 10
Model Sum ofSquares
df MeanSquare
F Sig.
1 Regression 1.158E-02 1 1.158E-02 14.806 .000
Residual 5.238E-02 67 7.818E-04
Total 6.395E-02 68
Predictors: (Constant), NSEMONTHDependent Variable: BSEMONTH
Coefficients
Unstandardi
zedCoefficients
Standardize
dCoefficients
t Sig.
Model B Std. Error Beta
1 (Constant) 1.200E-03 .003 .354 .724
NSEMONTH .372 .097 .425 3.848 .000
Dependent Variable: BSEMONTH
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General rule of Cointegration:-
The Grangers Cointegration test has been conducted by running the OLS
Regression equations. The residuals have been obtained for BSE & NSE monthly
from the estimated equations. Then the Unit Root test has been done to check the
Stationarity of residual series. The ADF calculated statistics shows that there is no
Unit Root. If the residuals do not have Unit Roots, then the series is said to be
Cointedgrated at I (1). Therefore the series is Cointegrated at I (1,0) and I (1,12). It
is bidirectional with reference to ANOVA TABLE 10.
TABLE 11: ADF UNIT ROOT TEST Y ON X
LAGS CONSTRAINTS ADF
VALUES
SIGNIFICANCE
(%)
CRITICAL
VALUES
1 -2.5968
5 -1.9452
0 FIRST
LEVEL OF
DIFFERENCE
Y ON X -10.22153
10 -1.6183
1 -2.6048
5 -1.9465
12 SECOND
LEVEL OF
DIFFERENCE
Y ON X -5.081737
10 -1.6189
Level of significance graph
Hypothesis:
H0 = ADF > critical values -- not reject hull hypothesis i.e., unit root exists.
H1 = ADF < critical values reject null hypothesis i.e. unit root does not exist.
INTERPRETATION:-
For ADF test statistic at 0 lags:-The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist we can say that BSE and NSE are cointegrated.
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For ADF test statistic at 12 lags:-
The ADF test statistics at 0 lags indicates that data is stationary at all the significant
levels such as 1%, 5%, 10%. Since the critical values are greater than the ADF test
statistics the data is stationary. Therefore the null hypothesis is rejected and we accept the
alternative hypothesis indicating that the data is stationary. Therefore unit root does not
exist we can say that BSE and NSE are cointegrated.
Regression analysis:-ANOVA TABLE 12
Model Sum ofSquares
df MeanSquare
F Sig.
1 Regression 1.516E-02 1 1.516E-02 14.806 .000
Residual 6.860E-02 67 1.024E-03Total 8.376E-02 68
Predictors: (Constant), BSEMONTHDependent Variable: NSEMONTH
Coefficients
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Model B Std. Error Beta
1 (Constant) 2.544E-03 .004 .658 .513
BSEMONTH .487 .127 .425 3.848 .000
Dependent Variable: NSEMONTH
General rule of Cointegration:-
The Grangers Cointegration test has been conducted by running the OLS
Regression equations. The residuals have been obtained for BSE & NSE monthly
from the estimated equations. Then the Unit Root test has been done to check the
Stationarity of residual series. The ADF calculated statistics shows that there is no
Unit Root. If the residuals do not have Unit Roots, then the series is said to be
Cointegrated at I (1). Therefore the series is Cointegrated at I (1,0) and I (1,12). It is
bidirectional with reference to ANOVA TABLE 12.
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Conclusions:-
We check the data series for stationarity by Augmented Dickey-Fuller unit root test. A
data series is said to be stationary if its mean variance are constant. The time series both
BSE and NSE were stationary which supports that the series can be used for further
analysis.
There are many factors which are affecting the price cointegration such as the
information flows from one market to another market. The results are very useful to
regulators as well as to market participants NSE used to follow accounting period
settlement starting from Wednesday and ending on the following Tuesday. Wednesday
being the first day it is advantageous for traders to buy / sell and keep the position opens
till next Tuesday. Investors get longest possible period without full investment. Where as,
BSE used to follow Monday to Friday accounting period settlement. Owing to this
different accounting period settlement there were arbitrage opportunities available.
By using the Engel-Granger the study finds that there is sufficient evidence of long-run
relationships between BSE Sensex and S&P Nifty for different lags i.e. 0 and 12.
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ADF Test Statistic -35.77700 1% Critical Value* -2.5671
5% Critical Value -1.9396
10% Critical Value -1.6157
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(BSEDAILY)
Method: Least Squares
Date: 06/18/06 Time: 14:00
Sample(adjusted): 1/04/2000 9/20/2005
Included observations: 1491 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
BSEDAILY(-1) -0.923621 0.025816 -35.77700 0.0000
R-squared 0.462093 Mean dependent var -3.89E-06
Adjusted R-squared 0.462093 S.D. dependent var 0.009009
S.E. of regression 0.006607 Akaike info criterion -7.200665
Sum squared resid 0.065045 Schwarz criterion -7.197106
Log likelihood 5369.096 Durbin-Watson stat 1.988115
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-0.06
-0.04
-0.02
0.00
0.02
0.04
1/03/00 12/03/01 11/03/03 10/03/05
BSEDAILY
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ADF Test Statistic -10.52569 1% Critical Value* -2.56715% Critical Value -1.9396
10% Critical Value -1.6157
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(BSEDAILY)
Method: Least Squares
Date: 06/18/06 Time: 14:01Sample(adjusted): 1/20/2000 9/20/2005
Included observations: 1479 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
BSEDAILY(-1) -0.904771 0.085958 -10.52569 0.0000
D(BSEDAILY(-1)) 0.000188 0.082731 0.002270 0.9982
D(BSEDAILY(-2)) -0.043580 0.079471 -0.548371 0.5835
D(BSEDAILY(-3)) -0.035484 0.076243 -0.465415 0.6417
D(BSEDAILY(-4)) 0.043481 0.072703 0.598055 0.5499
D(BSEDAILY(-5)) 0.003211 0.068497 0.046884 0.9626D(BSEDAILY(-6)) -0.042231 0.064207 -0.657727 0.5108
D(BSEDAILY(-7)) -0.008635 0.059265 -0.145693 0.8842
D(BSEDAILY(-8)) -0.030226 0.054371 -0.555919 0.5784
D(BSEDAILY(-9)) 0.025690 0.049562 0.518336 0.6043
D(BSEDAILY(-10)) 0.045875 0.042979 1.067369 0.2860
D(BSEDAILY(-11)) 0.023634 0.035204 0.671336 0.5021
D(BSEDAILY(-12)) 0.007140 0.025952 0.275118 0.7833
R-squared 0.465327 Mean dependent var 8.98E-06
Adjusted R-squared 0.460951 S.D. dependent var 0.008922S.E. of regression 0.006550 Akaike info criterion -7.209810
Sum squared resid 0.062904 Schwarz criterion -7.163233
Log likelihood 5344.655 Durbin-Watson stat 1.997350
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-0.06
-0.04
-0.02
0.00
0.02
0.04
1/03/00 12/03/01 11/03/03 10/03/05
BSEDAILY
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ADF Test Statistic -35.92243 1% Critical Value* -2.5671
5% Critical Value -1.9396
10% Critical Value -1.6157
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(XONY,2)
Method: Least Squares
Date: 06/18/06 Time: 13:26
Sample(adjusted): 1/05/2000 9/21/2005
Included observations: 1491 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(XONY(-1)) -0.927734 0.025826 -35.92243 0.0000
R-squared 0.464110 Mean dependent var -0.027794
Adjusted R-squared 0.464110 S.D. dependent var 98.87146
S.E. of regression 72.37837 Akaike info criterion 11.40236
Sum squared resid 7805557. Schwarz criterion 11.40592
Log likelihood -8499.461 Durbin-Watson stat 1.985296
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2000
4000
6000
8000
10000
1/03/00 12/03/01 11/03/03 10/03/05
XONY
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ADF Test Statistic -10.56207 1% Critical Value* -2.56715% Critical Value -1.9396
10% Critical Value -1.6157
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(XONY,2)
Method: Least Squares
Date: 06/18/06 Time: 13:30
Sample(adjusted): 1/21/2000 9/21/2005
Included observations: 1479 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(XONY(-1)) -0.907319 0.085904 -10.56207 0.0000
D(XONY(-1),2) 0.006444 0.082767 0.077861 0.9379
D(XONY(-2),2) -0.050881 0.079542 -0.639667 0.5225
D(XONY(-3),2) -0.028927 0.076366 -0.378792 0.7049
D(XONY(-4),2) 0.048135 0.072752 0.661622 0.5083
D(XONY(-5),2) 0.004309 0.068447 0.062947 0.9498
D(XONY(-6),2) -0.041849 0.064310 -0.650739 0.5153
D(XONY(-7),2) 0.010654 0.059372 0.179436 0.8576
D(XONY(-8),2) -0.039617 0.054500 -0.726912 0.4674
D(XONY(-9),2) 0.018936 0.049751 0.380611 0.7035
D(XONY(-10),2) 0.055764 0.043182 1.291366 0.1968
D(XONY(-11),2) 0.031583 0.035282 0.895147 0.3709
D(XONY(-12),2) 0.023134 0.026035 0.888605 0.3744
R-squared 0.469182 Mean dependent var 0.129436
Adjusted R-squared 0.464837 S.D. dependent var 97.58606
S.E. of regression 71.38892 Akaike info criterion 11.38291
Sum squared resid 7471290. Schwarz criterion 11.42949
Log likelihood -8404.664 Durbin-Watson stat 1.995723
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4000
6000
8000
10000
1/03/00 12/03/01 11/03/03 10/03/05
XONY
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ADF Test Statistic -35.78971 1% Critical Value* -2.5671
5% Critical Value -1.9396
10% Critical Value -1.6157
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(YONX,2)
Method: Least Squares
Date: 06/18/06 Time: 13:35
Sample(adjusted): 1/05/2000 9/21/2005
Included observations: 1491 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(YONX(-1)) -0.924866 0.025842 -35.78971 0.0000
R-squared 0.462269 Mean dependent var 0.004002
Adjusted R-squared 0.462269 S.D. dependent var 30.75121
S.E. of regression 22.54990 Akaike info criterion 9.070009
Sum squared resid 757662.2 Schwarz criterion 9.073569
Log likelihood -6760.692 Durbin-Watson stat 1.973360
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ADF Test Statistic -11.61969 1% Critical Value* -2.5671
5% Critical Value -1.9396
10% Critical Value -1.6157
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(YONX,2)
Method: Least Squares
Date: 06/18/06 Time: 13:40
Sample(adjusted): 1/21/2000 9/21/2005
Included observations: 1479 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(YONX(-1)) -1.072493 0.092300 -11.61969 0.0000
D(YONX(-1),2) 0.169153 0.088044 1.921236 0.0549
D(YONX(-2),2) 0.049822 0.084187 0.591795 0.5541
D(YONX(-3),2) 0.091556 0.080446 1.138104 0.2553
D(YONX(-4),2) 0.134980 0.076081 1.774157 0.0762
D(YONX(-5),2) 0.130492 0.071371 1.828372 0.0677
D(YONX(-6),2) 0.095006 0.066820 1.421809 0.1553
D(YONX(-7),2) 0.103239 0.061707 1.673055 0.0945
D(YONX(-8),2) 0.054258 0.056648 0.957808 0.3383
D(YONX(-9),2) 0.070304 0.051122 1.375224 0.1693
D(YONX(-10),2) 0.129067 0.044176 2.921689 0.0035
D(YONX(-11),2) 0.075151 0.035335 2.126789 0.0336
D(YONX(-12),2) 0.018005 0.026125 0.689210 0.4908
R-squared 0.477158 Mean dependent var 0.047670
Adjusted R-squared 0.472878 S.D. dependent var 30.59892
S.E. of regression 22.21578 Akaike info criterion 9.048233
Sum squared resid 723530.7 Schwarz criterion 9.094811Log likelihood -6678.169 Durbin-Watson stat 1.994124
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400
800
1200
1600
2000
2400
1/03/00 12/03/01 11/03/03 10/03/05
YONX
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ADF Test Statistic -7.818444 1% Critical Value* -2.5968
5% Critical Value -1.9452
10% Critical Value -1.6183
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(XONY,2)
Method: Least Squares
Date: 06/18/06 Time: 13:43
Sample(adjusted): 2000:03 2005:10
Included observations: 68 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(XONY(-1)) -0.999719 0.127867 -7.818444 0.0000
R-squared 0.476502 Mean dependent var -14.88971
Adjusted R-squared 0.476502 S.D. dependent var 449.1691
S.E. of regression 324.9879 Akaike info criterion 14.42005
Sum squared resid 7076349. Schwarz criterion 14.45269
Log likelihood -489.2817 Durbin-Watson stat 1.861825
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2000
3000
4000
5000
6000
7000
8000
2000 2001 2002 2003 2004 2005
XONY
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ADF Test Statistic -3.317427 1% Critical Value* -2.6048
5% Critical Value -1.9465
10% Critical Value -1.6189
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(XONY,3)
Method: Least Squares
Date: 06/18/06 Time: 13:46
Sample(adjusted): 2001:04 2005:10
Included observations: 55 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(XONY(-1),2) -8.688357 2.619005 -3.317427 0.0019
D(XONY(-1),3) 6.684659 2.542637 2.629026 0.0119
D(XONY(-2),3) 5.864413 2.397331 2.446226 0.0187
D(XONY(-3),3) 5.148280 2.200984 2.339081 0.0242
D(XONY(-4),3) 4.469174 1.986172 2.250144 0.0297
D(XONY(-5),3) 3.523455 1.777164 1.982628 0.0540
D(XONY(-6),3) 2.806212 1.560637 1.798120 0.0793
D(XONY(-7),3) 2.193991 1.336596 1.641477 0.1082
D(XONY(-8),3) 1.493572 1.099031 1.358989 0.1814
D(XONY(-9),3) 0.874570 0.861087 1.015658 0.3156
D(XONY(-10),3) 0.481749 0.617843 0.779728 0.4399
D(XONY(-11),3) 0.272711 0.381816 0.714249 0.4790
D(XONY(-12),3) 0.134952 0.168477 0.801015 0.4276
R-squared 0.837786 Mean dependent var -18.91245
Adjusted R-squared 0.791439 S.D. dependent var 742.3407
S.E. of regression 339.0159 Akaike info criterion 14.69303
Sum squared resid 4827134. Schwarz criterion 15.16750
Log likelihood -391.0585 Durbin-Watson stat 1.816052
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2000
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4000
5000
6000
7000
8000
2000 2001 2002 2003 2004 2005
XONY
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67/73
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ADF Test Statistic -10.22153 1% Critical Value* -2.5968
5% Critical Value -1.9452
10% Critical Value -1.6183
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(YONX,2)
Method: Least Squares
Date: 06/18/06 Time: 13:48
Sample(adjusted): 2000:03 2005:10
Included observations: 68 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(YONX(-1)) -1.303646 0.127539 -10.22153 0.0000
R-squared 0.608959 Mean dependent var 5.759899
Adjusted R-squared 0.608959 S.D. dependent var 201.4417
S.E. of regression 125.9681 Akaike info criterion 12.52453
Sum squared resid 1063153. Schwarz criterion 12.55717
Log likelihood -424.8340 Durbin-Watson stat 2.005896
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400
200
0
200
400
2000 2001 2002 2003 2004 2005
YONX
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