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In this paper, a new error innovation distribution was proposed in estimating some heteroscedasticity models. A new error innovation distribution was proposed called Exponentiated skewed student t distribution (ESSTD) and compared with the existing error distributions with an empirical dataset using daily returns on Nigeria Stock Exchange (NSE) index return from 30/08/2007 to 30/08/2017.The data shows stationarity at level without difference data and the ADF statistic shows evidence of stationarity, there is presence of ARCH effect. The estimate of the GARCH models and its extension shows a significant probability at 1%, 5% and 10% confident intervals forthe new error distribution and the existing distributions. The AIC and RMSE shows that the new error distributions outperformed in terms of fitness and forecasting evaluation with the smallest AIC and RMSE values respectively.

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