Estimating and Forecasting APARCH-Skew-t Models by Wavelet Support Vector Machines

This paper concentrates on comparing estimation and forecasting ability of Quasi-Maximum Likelihood (QML) and Support Vector Machines (SVM) for financial data. The financial series are fitted into a family of Asymmetric Power ARCH (APARCH) models. As the skewness and kurtosis are common characteristics of the financial series, a skew t distributed innovation is assumed to model the fat tail and asymmetry. Prior research indicates that the QML estimator for the APARCH model is inefficient when the data distribution shows departure from normality, so the current paper utilizes the nonparametric-based SVM method and shows that it is more efficient than the QML under the skewed Student's t-distributed error. As the SVM is a kernel-based technique, we further investigate its performance by applying a Gaussian kernel and a wavelet kernel. The wavelet kernel is chosen due to its ability to capture the localized volatility clustering in the APGARCH model. The results are evaluated by a Monte Carlo experiment, with accuracy measured by Normalized Mean Square Error ( NMSE ). The results suggest that the SVM based method generally performs better than QML, with a consistently lower NMSE for both in sample and out of sample data. The outcomes also highlight the fact that the wavelet kernel outperforms the Gaussian kernel with a lower NMSE , is more computation efficient and has better generation capability.