A re-examination of the asymmetric power ARCH model

The purpose of this paper is to provide a comprehensive methodology for the analysis of the Asymmetric Power ARCH model. First, it gives the ARMA representations of a power transformation of the conditional variance and the absolute returns. Second, it derives a certain fractional moment of the absolute observations. Third, it obtains the autocorrelation function of the power-transformed absolute returns. Finally, the practical implications of the results are illustrated empirically using daily data on five East Asia stock indices.