Testing the Random Walk Hypothesis: Power versus Frequency of Observation
Power functions of tests of the random walk hypothesis versus stationary ﬁrst order autoregressive alternatives are tabulated for samples of ﬁxed span but various frequencies of observation. For a t -test and normalized test, power is found to depend, for a substantial range of parameter values, more on the span of the data in time than on the number of observations. For a runs test, power rapidly declines as the number of observations is increased beyond a certain point.
Shiller, Robert J. and Perron, Pierre, "Testing the Random Walk Hypothesis: Power versus Frequency of Observation" (1984). Cowles Foundation Discussion Papers. 972.