A Comparative APARCH Volatility Study of International Markets

Abstract

This paper compares the daily return volatility by four leading international indices: JSE Top 40, FTSE 100, Nikkei 225 and S&P/ASX 200. The return series are modelled in ARMA process, where ARMA(1,3) values are taken for JSE Top 40 and S&P/ASX 200, ARMA(0,0) for FTSE 100, and ARMA(1,2) for Nikkei 225. The volatility is modelled in APARCH and GJR-GARCH (e.g., under various conditional distributions including Student-t (STD), skewed Student-t (SSTD), generalised error distribution (GED), skewed generalised error distribution (SGED), and generalised hyperbolic distribution (GHYD)). Model selection results based on information criteria indicate that the APARCH models outperform their GJR-GARCH counterparts in all cases. In particular, the ARMA(p,q)-APARCH(1,1) with SSTD is most suitable for the JSE Top 40 and the FTSE 100. The model that best describes the Nikkei 225 is an ARMA(1,2)–APARCH(1,1) model with SGED, and the S&P/ASX 200 fits an ARMA(1,3)-APARCH(1,1) model with GHYP. Among the indices, the FTSE 100 has the highest volatility persistence, while the Nikkei 225 responds more quickly to shocks. This out-of-sample forecasting test shows that ARMA(p,q)-APARCH(p,q) provides more accurate volatility predictions, especially for JSE Top 40 and S&P/ASX 200 investors.