Using Daily High/Low Time to Test for Intraday Random Walk in Two Index Futures Markets

This paper investigates the time of the daily high/low price in the Hang Seng and S&P 500 index futures and uses it to test for deviation from the predictive behavior of an intraday random walk model. Theoretical distributions of the daily high/low time under the random walk model are derived assuming either uniform or time-varying intraday trading speed. We show that under a random walk model, daily high/low time is more likely to occur near market open/close than in the middle of the trading day. Empirical distributions of the daily high/low time are compared with its theoretical distributions to test for the random walk model. It is found that for the intraday movement of the S&P 500 futures, the random walk hypothesis cannot be rejected. However, it is discovered that in the Hong Kong market, daily high/low time tends to appear significantly more often than is predicted by the random walk model in the first 15-minute time interval when the market opens in the morning or in the afternoon. The results remain valid even after we have taken the time-varying trading speed into account. By comparing the price behavior across markets, we can better understand the microstructure of the futures market.