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.