Application of Asymmetric-GARCH Type Models to The Kenyan Exchange Rates

Abstract

Modelling and forecasting the volatility of a financial time series has become essential in many economic and financial applications like portfolio optimization and risk management. The symmetric-GARCH type models can capture volatility and leptokurtosis. However, the models fail to capture leverage effects, volatility clustering, and the thick tail property of high-frequency financial time series. The main objective of this study was to apply the asymmetric-GARCH type models to Kenyan exchange to overcome the shortcomings of symmetric-GARCH type models. The study compared the asymmetric Conditional Heteroskedasticity class of models: EGARCH, TGARCH, APARCH, GJR-GARCH, and IGARCH. Secondary data on the exchange rate from January 1993 to June 2021 were obtained from the Central Bank of Kenya website. The best fit model is determined based on parsimony of the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Log-Likelihood criterion, and minimisation of prediction production errors (Mean error [ME] and Root Mean Absolute error [RMAE]). The optimal variance equation for the exchange rates data was APARCH (1,1) - ARMA (3,0) model with a skewed normal distribution (AIC = -4.6871, BIC = -4.5860). Volatility clustering was present in exchange rate data with evidence of the leverage effect. Estimated Kenya’s exchange rate volatility narrows over time, indicating sustained exchange rate stability.