The current study investigates the behaviour of time-varying parameters that are based on the score function of the predictive model density at time t. The mechanism to update the parameters over time is the scaled score of the likelihood function. The results revealed that there is high persistence of time-varying, as the location parameter is higher and the skewness parameter implied the departure of scale parameter from the normality with the unconditional parameter as 1.5. The results also revealed that there is a perseverance of the leptokurtic behaviour in stock returns which implies the returns are heavily tailed. Prior to model estimation, the White Neural Network test exposed that the stock price can be modelled by a GAS model. Finally, we proposed further researches specifically to model the existence of time-varying parameters with a more detailed model that encounters the heavy tail distribution of the series and computes the risk measure associated with the returns.<\/p>\r\n","references":"[1]\tArdia, D., K. Boudt, and L. Catania, Generalized Autoregressive Score Models in R: The GAS Package. 2016.\r\n[2]\tBernardi, M. and L. Catania, Switching-GAS copula models for systemic risk assessment. arXiv preprint arXiv:1504.03733, 2015.\r\n[3]\tCreal, D., S. J. Koopman, and A. Lucas, A dynamic multivariate heavy-tailed model for time-varying volatilities and correlations. Journal of Business & Economic Statistics, 2011. 29(4): p. 552-563.\r\n[4]\tCreal, D., S. J. Koopman, and A. Lucas, Generalized autoregressive score models with applications. Journal of Applied Econometrics, 2013. 28(5): p. 777-795.\r\n[5]\tEngle, R. F., Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 1982: p. 987-1007.\r\n[6]\tHarvey, A. C., Dynamic models for volatility and heavy tails: with applications to financial and economic time series. Vol. 52. 2013: Cambridge University Press.\r\n[7]\tJanus, P., S. J. Koopman, and A. Lucas, Long memory dynamics for multivariate dependence under heavy tails. Journal of Empirical Finance, 2014. 29: p. 187-206.\r\n[8]\tJarque, C. M. and A. K. Bera, Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics letters, 1980. 6(3): p. 255-259.\r\n[9]\tLucas, A., B. Schwaab, and X. Zhang, Conditional euro area sovereign default risk. Journal of Business & Economic Statistics, 2014. 32(2): p. 271-284.\r\n[10]\tMakatjane, K., N. Moroke, and D. Xaba, Threshold Cointegration and Nonlinear Causality test between Inflation Rate and Repo Rate. Journal of Economics and Behavioral Studies, 2017. 9(3): p. 163-170.\r\n[11]\tMakatjane, K. D. and N. D. Moroke, Comparative Study of Holt-Winters Triple Exponential Smoothing and Seasonal Arima: Forecasting Short Term Seasonal Car Sales in South Africa. 2016.\r\n[12]\tMakatjane, K. D. and T. J. Makatjane, Factors that Associated with the Academic performance of First year Students at the National University of Lesotho: Structural Equation Modelling Approach. International Journal of Statistics and Applied Mathematics, 2017. 2(1): p. 42-49.\r\n[13]\tOpschoor, A., et al., New HEAVY models for fat-tailed realized covariances and returns. Journal of Business & Economic Statistics, 2017: p. 1-15.\r\n[14]\tRamsey, J. B., Tests for specification errors in classical linear least-squares regression analysis. Journal of the Royal Statistical Society. Series B (Methodological), 1969: p. 350-371.\r\n[15]\tWentzel, D. and E. Mare, Extreme value theory\u2014An application to the South African equity market. Investment Analysts Journal, 2007. 36(66): p. 73-77.\r\n[16]\tWhite, H. An additional hidden unit test for neglected nonlinearity in multilayer feedforward networks. in Proceedings of the international joint conference on neural networks. 1989. Washington, DC.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 131, 2017"}