Impact Study Of Modeling And Forecasting Financial Assets Volatility Dynamics With Asymmetric Power ARCH (APARCH) Models. (A Case Of The S&P 500 Stock Index And The Sierra Leone Exchange Rate)

Modeling and forecasting of financial assets returns has been vital in providing accurate decision for future performance of market participant to appropriately invest in the financial market in order to maximize profit. Despite advances in literature in relation to modeling and forecasting the volatility dynamics of financial assets, the question as to whether modeling and forecasting the volatility of financial asset play a critical role in Mathematical finance, financial econometrics, financial economics, statistical application and the economic growth of the financial market remains an unsettled puzzle. This study therefore, examines volatility models for modeling and forecasting the Standard & Poor 500 daily stock index and the Sierra Leone monthly exchange rate returns, including the Autoregressive Moving Average (ARMA), the generalized autoregressive conditional heteroscedasticity (GARCH), the Taylor and Schwert Generalized Autoregressive Conditional Heteroscedasticity (GARCH), the Glosten, Jagannathan and Runkle GARCH, and the Asymmetric Power ARCH (APARCH) with the conditional distributions:normal, Student's t, and skewed Student's t-distributions.In addition, unit root (augmented Dickey-Fuller and Phillip-Perron) tests, co-integration test and Error Correction Model (ECM) were analyzed. The stationary APARCH (p) model with parameters was studied and the uniform convergence, strong consistency and asymptotic normality have been proven under simple ordered restriction, derived the analytical score expressions of the parameters of the APARCH model and the fractional moments and autocorrelation function. The properties of the GARCH process are derived taking into consideration the quasi-maximum likelihood estimation.In fitting these models to the (S&P)'s 500 daily stock index return data over the period 1st January 2002 to 31st December 2012 and the Sierra Leone monthly exchange rate return data for the period 1st January 1991 to 31st December 2013, the results revealed that the APARCH model with a skewed Student's t-distribution is the most effective and successful for modeling and forecasting the daily stock index returns series, while the GJR-GARCH model under the skewed Student's t-distribution provides the most effective estimates for modeling and forecasting the volatility of the Sierra Leone monthly exchange rate returns series. The error correction model results reveals that when the long-run equilibrium deviates then the daily stock index and the monthly exchange rate adjusts to restore equilibrium by rectifying the disequilibrium.Finally, the study suggests that the given models are suitable for modeling the (S & P)'s 500 daily stock index and the Sierra Leone monthly exchange rate volatility dynamics and the Asymmetric GARCH models captures asymmetric and leverage effect in the returns series. The Asymmetric (GARCH) and GARCH models better fits under the non-normal distribution than the normal distribution and improves the overall estimation for measuring conditional variance. Given the implication of stock index and exchange rate volatility, the findings of this study provides great benefits to policy makers, investors and researchers in promoting development and in managing risk of the financial and foreign exchange markets for achieving macroeconomic stability in emerging economies.