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Using a test statistic which specifically allows for parameter shifts over time, we investigate the time-variance relationship of security returns. The null hypothesis of stationary and independent increments is rejected, and the existence of a complex shortterm reversal phenomenon is reported. THIS PAPER DEALS WITH the compounding of security returns over time: every returns-generating process that has been proposed implies some specific relationship among returns as the time horizon increases, and these implications have not been adequately investigated. We focus specifically on the relationship between the variance of return and the time period over which that return is measured, and conduct a test of the common assumption that security returns are generated by a stochastic process which has stationary and independent increments. The test statistic which is used has been designed to allow for parameter shifts, and hence the results are quite general. The primary conclusions are that (1) this stochastic process does not have stationary and independent increments; (2) the observed discrepancies cannot be explained by any simple mechanism such as the presence of first-order serial correlation; and (3) there exists a complex short-term reversal phenomenon (which we quantify) which is unexplained by all of the existing models for this process.The organization of the rest of the paper is as follows: Section I contains a brief review of previous research; Section II describes the hypothesis and test statistic; Section III discusses the data which were used; Section IV reviews the empirical results; and Section V contains a brief summary. I. Previous ResearchThe topics studied in this paper are not new ones, although previous work has not been very extensive. This section briefly reviews the literature in this field, with emphasis on the most recent work.

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