Modelling Financial Market Volatility Using Asymmetric-Skewed-ARFIMAX and -HARX Models

Abstract

Extended heterogeneous autoregressive (HAR) and fractionally integrated autoregressive moving average (ARFIMA) models are introduced to model the S&P 500 index using various realized volatilities. The alternative robust-jump realized volatilities for this study include the tripower variation volatility, minimum and median nearest neighbor truncation (NNT) representations which are able to smooth or eliminate the abrupt jumps in consecutive observations. In order to capture clustering volatility and asymmetric of various realized volatilities, the HAR and ARFIMA model are extended with asymmetric GARCH threshold specification. In addition, the asymmetric innovations of various realized volatility are characterized by a skewed student-t distributions. The empirical findings show that the extended model provides the best performing in-sample and out-of-sample forecast evaluations. Lastly, the forecasted results are used in the determination of value-at-risk for S&P 500 market. DOI: http://dx.doi.org/10.5755/j01.ee.27.4.13927