Modeling Heteroscedasticity of Discrete-Time Series in the Face of Excess Kurtosis
To tackle the influence of excess kurtosis (which is thought to be induced by outliers) on the distributions of the innovations, this study considered the presence of outliers in the data on daily closing prices of shares of Skye Bank, Sterling Bank, and Zenith Bank, starting from January 03, 2006 to November 24, 2016. The data consist of 2690 observations each obtained from the Nigerian Stock Exchange website. Our findings revealed that GARCH(1,1) model under normal distribution, EGARCH(1,1) model under normal distribution and EGARCH(1,1) model under student-t distribution fitted adequately to the returns of Skye Bank, Sterling Bank, and Zenith Bank, respectively. However, all the series possessed in their residuals excess kurtosis values of 132.8707, 80.3030, and 26.3794, respectively. Conversely, when the returns for the three banks were adjusted for outliers, we discovered that GARCH(1,1) model under the normal distribution fitted well to the returns of Skye Bank, EGARCH(1,1) model under student-t fitted well to the returns of Sterling Bank and Zenith Bank with the respective kurtosis values of 2.9465, 3.6829, and 3.5746 in their residuals. Thus, with the outliers taken into consideration, the coefficients of kurtosis are, approximately, mesokurtic as required by the normal distribution. Hence, it could be deduced that the problem related to excess kurtosis and the choice of distribution of innovations in modeling heteroscedasticity of discrete-time series could be tackled by accounting for the presence of outliers.
