Comparison of Aparch-Type Models: Does the Continuous and Jump Components of Realized Volatility Improve the Fitting?

Abstract

This study aims to extend an APARCH-X(1,1) model to the APARCH-CJ(1,1) by separating the exogenous variable X into two components: continuous and discontinuous (jump). The study was based on the application of models to 1-min intraday high-frequency data from the Tokyo Stock Price Index from 2004 to 2011, where its dependent variable is daily return and its exogenous variability is Realized Volatility. As a basic framework, the return errors follow a Normal distribution. An Adaptive Random Walk Metropolis (ARWM) method was constructed in the Markov Chain Monte Carlo algorithm to estimate model parameters so that the model fits the observed return time series. By visual inspection, the parameter trace plots showed good convergence of the Markov chains, indicating that the ARWM method is efficient in estimating the studied models. Based on the results of the Akaike Information Criterion for model fitting to data, this study found that APARCH-CJ(1,1) is inferior to APARCH(1,1).