Milton Abdul Thorlie

This article examines volatility models for modeling and forecasting the Standard & Poor 500 (S&P 500) daily stock index returns, including the autoregressive moving average, the Taylor and Schwert generalized autoregressive conditional heteroscedasticity (GARCH),
the Glosten, Jagannathan and Runkle GARCH and asymmetric power ARCH (APARCH) with the following conditional distributions: normal, Student’s t and skewed Student’s t-distributions. In addition, we undertake unit root (augmented Dickey–Fuller and Phillip–Perron)
tests, co-integration test and error correction model. We study the stationary APARCH (p) model with parameters, and the uniform convergence, strong consistency and asymptotic normality are prove under simple ordered restriction. In fitting these models to S&P 500
daily stock index return data over the period 1 January 2002 to 31 December 2012, we found that the APARCH model using a skewed Student’s t-distribution is the most effective and successful for modeling and forecasting the daily stock index returns series. The results of this study would be of great value to policy makers and investors in managing risk in stock markets trading.

This article examines the accuracy and forecasting performance of volatility models for the Leones/USA dollars exchange rate
return, including the ARMA, Generalized Autoregressive Conditional Heteroscedasticity (GARCH), and Asymmetric GARCH models
with normal and non-normal (student’s t and skewed Student t) distributions. In fitting these models to the monthly exchange rate returns
data over the period January 2004 to December 2013, we found that, the Asymmetric (GARCH) and GARCH model better fits under the
non-normal distribution than the normal distribution and improve the overall estimation for measuring conditional variance. The
GJR-GARCH model using the skewed Student t- distribution is most successful and better forecast the Sierra Leone exchange rate
volatility. Finally, the study suggests that the given models are suitable for modeling the exchange rate volatility of Sierra Leone and the
Asymmetric GARCH models shows asymmetric in exchange rate returns, resulting to the presence of leverage effect. Given the
implication of exchange rate volatility, the study would be of great value to policy makers, investors and researchers at home and abroad in
promoting development of the capital market and foreign exchange market stability in emerging economies.