Time series: theory and methods
Time series: theory and methods
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The recent discovery of the compass rose pattern (Crack and Ledoit J. Finance 51(2) (1996) 751) has sparked considerable interest among researchers. This paper explores the significance of the effect of the compass rose pattern on random walk tests and measures to what extent its influence may limit the performance of test statistics. We show that in general, the asymptotic theory of test statistics is invalid for transactions data. However, Monte Carlo simulations indicate that the impact of the pattern, measured by the empirical size, is visible for moderate size samples only when the tick/volatility ratio is above some threshold, a condition that is readily met with intraday but not daily or weekly returns.