A STUDY OF INTRADAY STOCK INDEX AND FUTURES PRICES USING MARKOV CHAINS

Abstract

This research examines the intraday property of the Nikkei 225 index and futures prices from January 1, 1993 to December 31, 1994. We use first and second-order Markov chains to study the transition structures of the intraday Nikkei 225 cash and futures data. Our results of negative autocorrelation in futures returns and positive autocorrelation in index returns are consistent with the bid-ask bounce model (Roll, 1984), and the nonsynchronous trading models (infrequent trading) as noted by Mackinlay and Ramaswamy (1988) and Miller. Muthuswamy and Whaley (1994). Using likelihood ratio test, we conclude that the successive price changes are dependent and therefore the series do not follow random walk, a result which was also confirmed by the exact order test. Employing long run probability matrix, it is shown that for both index and futures price volatilities, there is a U-shaped transition pattern in that the most probable transitions in the opening and closing times are those between higher volatilities. Using daily data, we accept the hypothesis that the periods of higher volatilities are also the periods of higher volumes, consistent with the information model (Admati and Pfleiderer, 1988). However, contrary to most of the literature, the Nikkei intraday bid-ask spread does not show a U-shaped pattern, and therefore there is no concurrency between the intraday Nikkei futures volatility and bid-ask spread. We also perform research on the mean reversion of the Nikkei basis changes and the futures price volatilities after the cash market closes. Our research shows that the Markov methodology provides an alternative to test the random walk hypothesis and is useful for intraday analysis compared to the often-used GMM method.