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Modeling the Volatility of Exchange Rate Currency using GARCH Model

Author

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  • Chaido Dritsaki

    (Department of Accounting and Finance, Western Macedonia University of Applied Sciences, Kila, Kozani, Greece)

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. Modelli di volatilità del tasso di cambio con l’utilizzo di un modello GARCH In questo articolo viene esaminata la volatilità del tasso di cambio Euro/dollaro USA tramite un modello GARCH. Accertato che ci sono degli effetti ARCH sul tasso di cambio Euro/dollaro USA, sono state effettuate delle stime ARCH (p), GARCH (p,q) e EGARCH(p,q) includendo questi effetti su un’equazione minima. Questi modelli sono stati stimati col metodo della massima somiglianza utilizzando queste distribuzioni: normale, t-student e distribuzione generalizzata di errore. La funzione logaritmica di verosomiglianza è stata massimizzata usando l’algoritmo di Marquardt (1963), al fine di cercare dei parametri ottimali per tutti i modelli. I risultati hanno evidenziato che il modello ARIMA (0,0,1)-EGARCH(1,1) con distribuzione generalizzata di errore è la migliore per descrivere i rendimenti del tasso di cambio e cogliere gli effetti leva. Infine, nell’utilizzo del modello di previsione ARIMA(0,0,1)-EGARCH(1,1) sono state usate sia la procedura dinamica che quella statica. Quest’ultima ha fornito risultati migliori sulla previsione rispetto a quella dinamica.

Suggested Citation

  • Chaido Dritsaki, 2019. "Modeling the Volatility of Exchange Rate Currency using GARCH Model," Economia Internazionale / International Economics, Camera di Commercio Industria Artigianato Agricoltura di Genova, vol. 72(2), pages 209-230.
    • Handle: RePEc:ris:ecoint:0846
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    3. Mandelbrot, Benoit B, 1972. "Correction of an Error in "The Variation of Certain Speculative Prices" (1963)," The Journal of Business, University of Chicago Press, vol. 45(4), pages 542-543, October.
    4. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. repec:bla:scandj:v:93:y:1991:i:1:p:53-73 is not listed on IDEAS
    7. N. Antonakakis & J. Darby, 2013. "Forecasting volatility in developing countries' nominal exchange returns," Applied Financial Economics, Taylor & Francis Journals, vol. 23(21), pages 1675-1691, November.
    8. Hsieh, David A., 1988. "The statistical properties of daily foreign exchange rates: 1974-1983," Journal of International Economics, Elsevier, vol. 24(1-2), pages 129-145, February.
    9. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    10. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    11. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    12. Friedman, Daniel & Vandersteel, Stoddard, 1982. "Short-run fluctuations in foreign exchange rates : Evidence from the data 1973-1979," Journal of International Economics, Elsevier, vol. 13(1-2), pages 171-186, August.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Melina Dritsaki & Chaido Dritsaki, 2020. "Forecasting European Union CO2 Emissions Using Autoregressive Integrated Moving Average-autoregressive Conditional Heteroscedasticity Models," International Journal of Energy Economics and Policy, Econjournals, vol. 10(4), pages 411-423.
    2. Usha Rekha Chinthapalli, 2021. "A Comparative Analysis on Probability of Volatility Clusters on Cryptocurrencies, and FOREX Currencies," JRFM, MDPI, vol. 14(7), pages 1-23, July.
    3. Ebrahim Merza & Imad A. Moosa, 2023. "Pitfalls in Econometric Forecasting with Illustrations from Exchange Rate Economics," Economia Internazionale / International Economics, Camera di Commercio Industria Artigianato Agricoltura di Genova, vol. 76(2), pages 147-172.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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