# 15-037/III/DSF90 (2015-03-19)

Siem Jan Koopman, VU University Amsterdam, the Netherlands; Rutger Lit, VU University Amsterdam, the Netherlands; André Lucas, VU University Amsterdam, the Netherlands
time-varying copulas, dynamic discrete data, score driven models, Skellam distribution, dynamic dependence
JEL codes:
C32, G11

We investigate the intraday dependence pattern between tick data of stock price changes using a new time-varying model for discrete copulas. We let parameters of both the marginal models and the copula vary over time using an observation driven
autoregressive updating scheme based on the score of the conditional probability mass function with respect to the time-varying parameters. We apply the model to high-frequency stock price changes expressed as discrete tick-size multiples for four liquid U.S. financial stocks. Our modeling framework is based on Skellam densities for the marginals and a range of different copula functions. We find evidence of intraday time-variation in the dependence structure. After the opening and before the close of the stock market, dependence levels are lower. We attribute this finding to more idiosyncratic trading at these times. The introduction of score driven dynamics in the dependence structure significantly increases the likelihood values of the time-varying copula model. By contrast, a fixed daily seasonal dependence pattern clearly fits the data less well.