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Alejandro Fonseca EGADE Business School, Campus Monterrey [email protected] Roberto J. Santillan -Salgado EGADE Business School, Campus Monterrey [email protected]. Increasing role of foreign exchange in corporate decision making has become a popular topic in modern economies. - PowerPoint PPT Presentation
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Alejandro FonsecaEGADE Business School, Campus Monterrey
Roberto J. Santillan-SalgadoEGADE Business School, Campus Monterrey
Increasing role of foreign exchange in corporate decision making has become a popular
topic in modern economies.
We examine the performance of several of the GARCH family models
(EGARCH,GARCH-M, TARCH, FIGARCH) in forecasting the volatility behavior of the peso-dollar exchange rate and finally taste the presence of LM in the
peso dolar xt.
“long memory“ model of exchange
rate return
XR Modelling
XR Volatility
Modelling
Long Memory Models(CWJ Granger, R Joyeux
1980,1996)
Long Memory Models(CWJ Granger, R Joyeux
1980,1996)
LM Models estimation(J Geweke, S Porter Hudak‐ 1983)
LM Models estimation(J Geweke, S Porter Hudak‐ 1983)
LMM & Stock markets(Z Ding, CWJ Granger, RF Engle 1993T Bollerslev, H Ole Mikkelsen 1996)
LMM & Stock markets(Z Ding, CWJ Granger, RF Engle 1993T Bollerslev, H Ole Mikkelsen 1996)
LM & Regime SwitchingFX Diebold, A Inoue 2001
LM & Regime SwitchingFX Diebold, A Inoue 2001
LM Processes and Fractional integration in
econometricsJ Gonzalo, C Granger 1995
LM Processes and Fractional integration in
econometricsJ Gonzalo, C Granger 1995
LM in Foreign XR´sYW Cheung, 1993LM in Foreign XR´sYW Cheung, 1993
LM detection and estimation in stochastic volatility
FJ Breidt, N Crato, P De Lima , 1998
LM detection and estimation in stochastic volatility
FJ Breidt, N Crato, P De Lima , 1998
Testing for long memory data
Variable Definition Source
1st dif nat log Peso dólar XR
Peso-Dólar XR Daily Banxico
Oxmetrics software academic edition
Eviews, 8th edition.
NCSS.
Testing for long memory data
Variable Definition Source
1st dif nat log Peso dólar XR
Peso-Dólar XR Daily Banxico
ARIMAGARCH
FIGARCH
0
500
1,000
1,500
2,000
2,500
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
Series: USDSample 5 5156Observations 5152
Mean 0.000276Median -9.64e-05Maximum 0.201137Minimum -0.159713Std. Dev. 0.009105Skewness 3.210588Kurtosis 107.1233
Jarque-Bera 2336194.Probability 0.000000
2
4
6
8
10
12
14
16
1994 1996 1998 2000 2002 2004 2006 2008 2010 2012
Graph 1 PesoDolar 11/08/93-6/21/13
-.20
-.15
-.10
-.05
.00
.05
.10
.15
.20
.25
1994 1996 1998 2000 2002 2004 2006 2008 2010 2012
Peso Dolar Daily returns 11/08/93-6/21/13
.00
.04
.08
.12
.16
.20
.24
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Peso Dolar absolute daily returns 11/08/93-6/21/13
• Normality Test Section of Peso Dólar returns • Test Prob 10% Critical 5% Critical Decision
• Test Name Value Level 10%Value 5%Value - 5% decision• Shapiro-Wilk W 0.615181 0 Reject normality • Anderson-Darling 339.0483 1 Can't reject normality • Martinez-Iglewicz 3.662488 0.994594 0.994536 Reject normality • Kolmogorov-Smirnov 0.158299 0.015 0.016 Reject normality • D'Agostino Skewness 49.87968 0 1.645 1.96 Reject normality • D'Agostino Kurtosis 45.3115 0 1.645 1.96 Reject normality • D'Agostino Omnibus 4541.117 0 4.605 5.991 Reject normality
Autocorrelacions of the (DlogPesodolar=Rpd)11/08/93-6/21/13Data Lags
1 2 3 4 5 10 20 40 70 100Rpd -0.04 0.01 -0 0.01 0.012 -0.03 0.059 0.022 0.007 -0.006absRpd 0.44 0.04 3420 0.38 0.327 0.24 0.204 0.157 0.036 0.001Rpd*Rpd 0.23 0.33 0.27 0.2 0.167 0.07 0.08 0.048 0 -0.005Rpd^0.5 0.4 0.38 0.38 0.36 0.322 0.27 0.207 0.177 0.089 0.042
• We find the presence of a long memory behavior in the data.
• Same as Taylor(1986) and Granger , et al(1993) we found that the return process is characterized by more correlation between squared returns or absolute values than there is between returns themselves.
• Series is not iid, contradicting eficient markets h´s.
• An introduction to long memory time series models and fractional differencing‐ , CWJ Granger, R Joyeux - Journal of time series analysis, 1980
• The estimation and application of long memory time series models, J Geweke, S Porter Hudak - ‐Journal of time series analysis, 1983
• Varieties of long memory models, CWJ Granger, Z Ding - Journal of econometrics• A long memory property of stock market returns and a new model, Z Ding, CWJ Granger, RF Engle -
Journal of empirical finance, 1993 • Long memory processes and fractional integration in econometrics, RT Baillie - Journal of
econometrics, 1996 • Modeling and pricing long memory in stock market volatility,T Bollerslev, H Ole Mikkelsen - Journal
of Econometrics, 1996 • The detection and estimation of long memory in stochastic volatility, FJ Breidt, N Crato, P De Lima -
Journal of econometrics• Long memory in foreign-exchange rates, YW Cheung - Journal of Business & Economic Statistics• On Estimation of Long –Memory Time Series Models , Y Yajima - Australian Journal of Statistics,
1985 • Modeling and pricing long memory in stock market volatility• T Bollerslev, H Ole Mikkelsen - Journal of Econometrics, 1996 - Elsevier
• Varieties of long memory models• CWJ Granger, Z Ding - Journal of econometrics, 1996 – Elsevier• A search for long memory in international stock market returns• YW Cheung, KS Lai - Journal of International Money and Finance, 1995 - Elsevier• Modelling financial time series, Taylor, S. 1986, N.Y. John Wiley & Sons.
• Statistical tests for whether a given set of independent, identically distributed draws comes from a specified probability density,Mark Tygert1,Communicated by Vladimir Rokhlin, Yale University, New Haven, CT, June 14, 2010 (received for review May 24, 2010).Procedings of the national academy of sciences of the USA.