Alejandro FonsecaEGADE Business School, Campus Monterrey

afonseca@itesm.mx

Roberto J. Santillan-SalgadoEGADE Business School, Campus Monterrey

roberto.santillan@itesm.mx

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.