Parameter Estimates of Conditional Volatility Models under Different Error Distributions: Monte Carlo Simulation Approach

Abstract

Aside from the overwhelming empirical data used for investigating the choice of error distributions in conditional volatility models (CVMs), many of the current studies do not use prespecified parameters for estimation and those that  have prespecified parameters are often applied to very few CVMs. This study addresses these gaps by conducting a comprehensive analysis via Monte Carlo simulation to generate financial series using prespecified parameter values based on different error distributions and examini the parameter estimates with five different CVMs.  The error distributions considered include the normal distribution (ND), student-t distribution (STD), skewed student-t distribution (SSTD), generalized error distribution (GED) and the skewed generalized error distribution (SGED), while the CVMs considered are SGARCH,  EGARCH, IGARCH,  GJRGARCH, and  PGARCH. The efficiency of the parameter estimates was assessed based on the log-likelihood (LL), AIC and BIC values. Initial results revealed that SGARCH is the best model for all sample sizes, considering the simulated returns that are not skewed and the tails seem to be normally distributed. However, in practice, it is assumed that the returns of financial series exhibit fat tail distributions, which are often skewed. To address these issues, STD, SSTD, GED, and SGED error assumptions were considered in the simulation of the GARCH (1,1) process. The results further showed that SGARCH under ND, EGARCH under STD, GJRGARCH under SSTD, EGARCH under GED, and GJRGARCH under SGED were the best models for all sample sizes considered.