Abstract
A fundamental statistical test of serial independence is developed and applied to daily stock returns. Let xt be the deviation of the daily return on a stock from its sample mean after any autocorrelation present has been removed. If xt is serially independent, then the cumulative sum of xt over time is the position of a one-dimensional random walk on a line. The empirical distribution of step lengths over a large sample allows the distribution of the largest absolute excursion in a T-step walk to be calculated by repeated simulation. The observed maximal excursions are found to be significantly smaller than one would expect, based on serial independence and the observed distribution of step lengths. It is concluded that these daily stock returns are not serially independent and that the market value of the corporations studied has a tendency to return to an interval around the trend value.
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