Recent Articles

Read more about our latest published articles.

Review’s Archive

Corresponding Author:
Chaido Dritsaki, Department of Accounting and Finance, Western Macedonia University of Applied Sciences, Kila, Kozani, Greece

Modeling the Volatility of Exchange Rate Currency using GARCH Model

Volume 72 - Issue 2, May 2019
(pp. 209-230)
JEL classification: C22, C32, C53
Keywords: Exchange Rate, Volatility, ARIMA-GARCH Models, Forecasting

Abstract

In this paper, we study GARCH models with their modifications in order to study the volatility of Euro/US dollar exchange rate. Given that there are ARCH effects on exchange rate returns Euro/US dollar, we estimated ARCH(p), GARCH(p,q) and EGARCH(p,q) including these effects on mean equation. These models were estimated with maximum likelihood method using the following distributions: normal, t-student and generalized error distribution. The log likelihood function was maximized using Marquardt’s algorithm (1963) in order to search for optimal parameter of all models. The results showed that ARIMA(0,0,1)-EGARCH(1,1) model with generalized error distribution is the best in order to describe exchange rate returns and also captures the leverage effect. Finally, for the forecasting of ARIMA(0,0,1)-EGARCH(1,1) model both the dynamic and static procedure is used. The static procedure provides better results on the forecasting rather than the dynamic.


Read the full article

Download the article in PDF format to read and print.


Bibliography

Abdalla, S.Z.S. (2012), “Modelling Exchange Rate Volatility using GARCH Models: Empirical Evidence from Arab Countries”, International Journal of Economics and Finance, 4(3), 216-229.
Antonakakis, N. and J. Darby (2012), “Forecasting Volatility in Developing Countries' Nominal Exchange Returns”, MPRA Working Paper No.40875.
Black, F. (1976), “Studies of Stock Price Volatility Changes”, Proceedings of the 1976 Meeting of the Business and Economics Statistics Section, American Statistical Association, Washington  DC, 177-181.
Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroskedasticity”, Journal of Econometrics, 31(3), 307-327.
Box, G.E.P. and G.M. Jenkins (1976), Time Series Analysis-Forecasting and Control,  Holden-Day: San Francisco.
Dickey, DA. and W.A. Fuller (1979), “Distributions of the Estimators for Autoregressive Time Series with a Unit Root”, Journal of American Statistical Association, 74(366), 427-431.
Dickey, DA. and W.A, Fuller (1981), “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root”, Econometrica, 49(4), 1057-1072.
Dritsaki, C. (2017), “An Empirical Evaluation in GARCH Volatility Modeling: Evidence from the Stockholm Stock Exchange”, Journal of Mathematical Finance, 7(2), 366-390.
Engle, R.F. (1982), “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation”, Econometrica, 50(4), 987-1008.
Epaphra, M. (2017), “Modeling Exchange Rate Volatility: Application of the GARCH and EGARCH Models”, Journal of Mathematical Finance, 7(1), 121-143.
Fama, E.F. (1965), “The Behavior of Stock Market Prices”, Journal of Business, 38(1), 34-105.
Friedman, D. and S. Vandersteel (1982), “Short-Run Fluctuations in Foreign Exchange Rates: Evidence from the Data 1973-1979”, Journal of International Economics, 13(1-2), 171-186.
Hsieh, D.A. (1988), “The Statistical Properties of Daily Foreign Exchange Rates: 1974-1983”, Journal of International Economics, 24(1-2), 129-145.
Jarque, C. and A. Bera (1980), “Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals”, Economics Letters, 6(3), 255-259.
Johnston, K. and E. Scott (2000), “GARCH Models and the Stochastic Process underlying Exchange Rate Price Changes”, Journal of Financial and Strategic Decisions, 13(2), 13-24.
Ljung G.M. and G.E.P. Box (1978), “On a Measure of Lack of Fit in Time Series Models”, Biometrika, 65(2), 297-303.
MacKinnon J.G. (1996), “Numerical Distribution Functions for Unit Root and Cointegration Tests”, Journal of Applied Econometrics, 11(6), 601-618.
Mandelbrot, B. (1963), “The Variation of Certain Speculative Prices”, Journal of Business, 36(4), 394-414.
Marquardt, D.W. (1963), “An Algorithm for Least Squares Estimation of Nonlinear Parameters”, Journal of the Society for Industrial and Applied Mathematics, 11(2), 431-441.
Miletić, S. (2015), “Modeling and Forecasting Exchange Rate Volatility: Comparison between EEC and Developed Countries”, Industrija, 43(1), 7-24.
Mundaca, B.G. (1991), “The Volatility of the Norwegian Currency Basket”, Scandinavian Journal of Economics, 93(1), 53-73.
Nelson, D.B. (1991), “Conditional Heteroscedasticity in Asset Returns: A New Approach”, Econometrica, 59(2), 347-370.
Newey, W.K. and K.D. West (1994), “Automatic Lag Selection in Covariance Matrix Estimation”, Review of Economic Studies, 61(4), 631-654. 
Phillips, P.C.B and P. Perron (1998), “Testing for a Unit Root in Time Series Regression”,  Biometrika, 75(2), 335-346.
Sandoval, J. (2006), “Do Asymmetric GARCH Models Fit better Exchange Rate Volatilities on Emerging Markets?”, Odeon, 3, 97-116, Universidad Externado de Colombia.
Taylor, S.J. (1986), Modeling Financial Time Series, Wiley: New York.
Theil, H. (1967), Economics and Information Theory, Rand McNally and Co, and North-Holland Publishing Company: Chicago and Amsterdam.
Vee, D.N.C., P.N. Gonpot and N. Sookia (2011), “Forecasting Volatility of USD/MUR Exchange Rate using a GARCH (1,1) Model with GED and Student’s-t errors”, University of Mauritius Research Journal, 17.
Yoon, S. and K.S. Lee (2008), “The Volatility and Asymmetry of Won/Dollar Exchange Rate”, Journal of Social Sciences, 4(1), 7-9.

Register your account

First-time users should click on “Register your account” and enter the requested information. Upon successful registration, you will receive an e-mail with instructions to verify your registration.

Submission Guidelines

Authors’ login

Use the assigned user ID and password to login. Please, do not register again. Usernames and passwords may be changed after.

Quick search by author:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Back to the top

Institute for International Economics
of the Genoa Chamber of Commerce


Istituto di Economia Internazionale
Camera di Commercio di Genova
Via Garibaldi, 4 (III piano) - 16124 Genova (Italy)
www.ge.camcom.gov.it