Modelling the Volatility of Exchange Rates in Rwandese Markets
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 6, November 2015, Pages: 426-431
Received: Aug. 15, 2014; Accepted: Mar. 19, 2015; Published: Sep. 25, 2015
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Authors
Jean de Dieu Ntawihebasenga, Mahatma Gandhi University-Rwanda, Faculty of Science, Department of Mathematics, Kigali-Rwanda
Joseph Kyalor Mung’atu, Jomo Kenyatta University of Agriculture and Technology, Faculty of Applied Science, Department of Statistics and Actuarial Science, Kisumu-Kenya
Peter Nyamuhanga Mwita, Jomo Kenyatta University of Agriculture and Technology, Faculty of Applied Science, Department of Statistics and Actuarial Science, Nairobi-Kenya
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Abstract
This work applied Generalized Autoregressive Conditional Heteroskedasticity (GARCH) approachto modelling volatility in Rwanda Exchange rate returns. The Autoregressive (AR) model with GARCH errors was fitted to the daily exchange rate returns using Quasi-Maximum Likelihood Estimation (Q-MLE) method to get the current volatility, asymptotic consistency and asymptotic normality of estimated parameters.Akaike Information criterion was used for appropriate GARCH model selection while Jarque Bera test used for normality testing revealed that both returns and residuals have fat tails behaviour. It was shown that the estimated model fits Rwanda exchange rate returns data well.
Keywords
Model, Volatility, ExchangeRate, Quasi Maximum Likelihood, GARCH Model
To cite this article
Jean de Dieu Ntawihebasenga, Joseph Kyalor Mung’atu, Peter Nyamuhanga Mwita, Modelling the Volatility of Exchange Rates in Rwandese Markets, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 426-431. doi: 10.11648/j.ajtas.20150406.12
References
[1]
Blum, P., & Dacorogna, M. (2002). Extreme Moves in Daily Foregn Exchange rates and risk limit setting. Department of Mathematics, General Guisan Quasi Vol.26 , 8092Z'urich.
[2]
Blum, P., & Dacorogna, M. (2002). Extreme moves in daily Foreign Exchange rates and risk limit setting. . Department of Mathematics General Guisan Quasi Vol26 , , 8092Z'urich.
[3]
Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroscedasticity . Journal of Econometris Vol.31 , 307-327.
[4]
Engle, F. (19982). Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation. Econometrica Vol.50 , 987-1008.
[5]
Franq, C., & Zakoian, J. (2004). Maximam Likelihood Estimationof Pure GARCH and ARMA-GARCH Processes . Bernoulli Vol.10 , 605-637.
[6]
Ghysels, E., Harvey, A., & Renault, E. (1996). Stochastic Volatility. In Handbook of Statistics. Statistical Methods in Finance, Maddala, G.S. Ed. North- Holland, Amsterdam Vol.14 , 119-91.
[7]
Glosten, L., Jagannathan, R., & Runkle, D. (1993). On the relation between the expected value and the Volatility of Nominal excess return on stocks. Journal of Finance Vol.48 , 1779-1801.
[8]
Hull, J., & White, A. (1998). Value at Risk When Changes in Market Variables are not Normally Distributed. Journal of Risk Vol.1 , 47-61.
[9]
Longin, F. (1996). The Asymptotic Distribution of Extreme Stock Market Returns . Journal of Business Vol.67 , 383-408.
[10]
Maan, I., Mwita, N. P., & Odhiambo, R. (2010). Modelling the Volatility of Exchange Rates in the Kenyan Markets. Journal of Business Management Vol.4 , 1401-1408.
[11]
Madura, J. (1989). International Financial Management 2nd Ed. St.Paul Minnesta: West Publishing Company.
[12]
Manganelli, S., & Engle, R. (2001). Value at Risk Models in Finance,European Central Bank Working Paper Series, Frankfurt. Modelling. Mathematical Finance Vol.14 , 75-102.
[13]
Neftci, S. (2000). Value at Risk Calculations, Extreme Events and Tail Estimation. Journal of Derivatives Vol.7 , 23-38.
[14]
Nelson, D. (1991). Conditional Heteroscedasticity in asset returns: A new Approach. Econometrica Vol.59 , 347-370.
[15]
Posedel, P. (2005). Properties and Estimation of GARCH(1,1) Model . Metodolo S Ki Zvezki Vol.2 , 243-257.
[16]
Sandmann, G., & Koopman, S. (1998). Estimation of Stochastics Volatility Models Via Monte Carlo Maximum Likelihood . Journal of Econometrics Vol.87 , 271-301.
[17]
Smith, W., Clifford, C., & Stykes, W. (1990). Managing Financial Risk. New York, Harper and Row.
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