Modeling Volatility under Normal and Student-t Distributional Assumptions (A Case Study of the Kenyan Exchange Rates)

Rotich Titus Kipkoech^1,

¹Department of Mathematics & Computer Science, University of Eldoret, Eldoret, Kenya

Cite this paper:
Rotich Titus Kipkoech. Modeling Volatility under Normal and Student-t Distributional Assumptions (A Case Study of the Kenyan Exchange Rates). American Journal of Applied Mathematics and Statistics. 2014; 2(4):179-184. doi: 10.12691/ajams-2-4-1

Abstract

The predictive performance of two EGARCH^{i} models for modeling daily changes in logarithmic exchange rates (log Rt^{ii}) are analyzed here. One is based on modeling the data on assumption of normal distribution and the other is based on the standardized student-t distribution. In particular, the (log Rt) of USDKES^{iii}, EUROKES^{iv} and GBPKES^{v} are considered. For each assumption EGARCH is fitted, with varying numbers of parameters, and attempt to replicate the empirical (log Rt) sequence via simulation. Assessing the fit of each model, it is concluded that the families of EGARCH models with t-innovations adequately reflect the empirical nature of the (log Rt) sequence and therefore provides a better prediction model.

Keywords:
EGARCH simulation exchange rates innovations

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References:

[1]	Alexakis, P., & Xanthakis, M. (1995). Day-of-the-week effect on the greek stock market. Applied Financial Economics, 5, 43-50.
[2]	Alexander, C. (2009). Practical Financial Econometrics. John Wiley & Sons Ltd.
[3]	Alexander, C., & Lazar, E. (2006). Normal Mixture GARCH (1,1): Application to exchange rate modeling. Journal of Applied Econometrics Economic Review, 39, 885-905.
[4]	Bollerslev, T. (1986). A generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307-327.
[5]	Bollerslev, T. (1987). A conditional heteroskedastic time series model for speculative rices and rates of return. review of economics and statistics, 69, 542-547.
[6]	Chang, S. (2012). Application of EGARCH model to estimate financial volatility of daily returns: The empirical case of china.
[7]	Drakos, A. A., Kouretas, G. P., & Zarangas, L. P. (2010). Forecasting financial volatility of the athens stock exchange daily returns: an application of the assymetric normal mixture GARCH model. International Journal of Finance and Economics, 1-4.
[8]	Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.
[9]	Engle, R. F., Bollerslev, T., & Nelson, D. B. (1994). Arch Models. Amsterdam: Handbook of Econometrics.
[10]	Maana, I., Mwita, P. N., & Odhiambo, R. (2010). Modelling the volatility of exchange rates in the kenyan market. African Journal of Business Management, 4(7), 1401-1408.
[11]	Nelson, D. B. (1991). Conditional heteroscedasticity in asset returns: a new approach. Econometrica, 59, 347-70.