Detection and Estimation of long memory in the Exchange rate volatility of the peso-dolar Alejandro...
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![Page 1: Detection and Estimation of long memory in the Exchange rate volatility of the peso-dolar Alejandro Fonseca EGADE Business School, Campus Monterrey afonseca@itesm.mx.](https://reader030.fdocuments.us/reader030/viewer/2022032606/56649eb15503460f94bb806f/html5/thumbnails/1.jpg)
Alejandro FonsecaEGADE Business School, Campus Monterrey
Roberto J. Santillan-SalgadoEGADE Business School, Campus Monterrey
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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
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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
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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.
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Testing for long memory data
Variable Definition Source
1st dif nat log Peso dólar XR
Peso-Dólar XR Daily Banxico
ARIMAGARCH
FIGARCH
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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
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2
4
6
8
10
12
14
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1994 1996 1998 2000 2002 2004 2006 2008 2010 2012
Graph 1 PesoDolar 11/08/93-6/21/13
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-.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
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.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
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• 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
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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
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• 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.
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• 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
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• 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.