Intraday periodicity in the relationship between the stock and stock index futures markets.

In this paper we study the effect of the intraday periodicity on the return volatilities in the stock market and stock index futures market on Ibex35. We estimate a periodic component for each market by using the Fourier flexible functional form, and then we use this component to filter returns. The effect of the periodicity is analyzed from fitting standard GARCH models to return series and from modelling the lead-lag relationship between both markets by using a vector error correction model with GARCH-BEKK errors changing over time, taking into account infrequent trading. Our data set consists of the Ibex35 intraday closing prices from January to November 2000, using sampling intervals of ten minutes. In general, the results indicate two facts. Firstly, intraday periodicity affects the estimated coefficients in the standard GARCH and multivariate volatility models. Secondly, the periodic patterns do not affect the lead-lag relationship between both markets, in the sense that we always observe causality in both directions and we always reject that volatilities are equal in both markets.