Periodic Stochastic Volatility and Fat Tails

Abstract

This article provides a comprehensive analysis of the size and statistical significance of the day of the week, month of the year, and holiday effects in daily stock index returns and volatility. We employ data from the Dow Jones Industrial Average (DJIA), the S&P 500, the S&P MidCap 400, and the S&P SmallCap 600 in order to test whether the seasonal patterns of medium and small firms are similar to those of large firms. Using formal hypothesis tests based on bootstrapping, we demonstrate that there are more significant calendar effects in volatility than in expected returns, especially for the two large cap indices. More importantly, we introduce the periodic stochastic volatility (PSV) model for characterizing the observed seasonal patterns of daily financial market volatility. We analyze the interaction between seasonal heteroskedasticity and fat tails by comparing the performance of Gaussian PSV and fat-tailed PSVt specifications to the plain vanilla SV and SVt benchmarks. Consistent with our model-free results, we find strong evidence of seasonal periodicity in volatility, which essentially eliminates the need for a fat-tailed conditional distribution, and is robust to the exclusion of the crash of 1987 outliers.

Keywords: stochastic volatility, calendar effects, seasonal heteroskedasticity, bootstrapping, Bayesian MCMC estimation