A Coupled Component GARCH Model for Intraday and Overnight Volatility

We propose a semi-parametric coupled component GARCH model for intraday and overnight volatility that allows the two intraday periods to have different properties. To capture the very heavy tails of overnight returns, a dynamic conditional score model with t innovations is adopted. We propose a several step estimation procedure that captures the nonparametric slowly moving components by kernel estimation and the dynamic parameters by estimated maximum likelihood. We establish the consistency and asymptotic normality of our semiparametric estimation procedures. We extend the modelling to the multivariate case where we allow time varying correlation between stocks. We apply our model to the study of the Dow Jones industrial average component stocks over the period 1991-2016 and the CRSP capitalization-based portfolios over the period 1992-2015. We show that the ratio of overnight to intraday volatility has actually increased in importance for Dow Jones stocks during the last two decades. This ratio has also increased for large stocks in CRSP, but decreased for small stocks in CRSP. Notably, the slope increases monotonically from the smallest cap decile to the largest cap decile. The multivariate model shows that overnight and intraday correlations have both increased considerably during this period