Spectral Based Testing of the Martingale Hypothesis

34 Pages Posted: 27 Jun 2007 Last revised: 2 Apr 2023

See all articles by Steven N. Durlauf

Steven N. Durlauf

University of Chicago; National Bureau of Economic Research (NBER); Korea Development Institute (KDI)

Date Written: April 1992

Abstract

This paper proposes a method of testing whether a time series is a martingale. The procedure develops an asymptotic theory for the shape of the spectral distribution function of the first differences. Under the null hypothesis, this shape should be a diagonal line. several tests are developed which determine whether the deviation of the sample spectral distribution function from a diagonal line, when treated as an element of a function space, is too erratic to be attributable to sampling error. These tests are consistent against all moving average alternatives. The testing procedure possesses the additional advantage that it eliminates discretion in choosing a particular H[sub 1] by the researcher and therefore guards against data mining, The tests may further be adjusted to analyze subsets of frequencies in isolation, which can enhance power against particular alternatives. Application of the test to stock prices finds some evidence against the random walk theory.

Suggested Citation

Durlauf, Steven N., Spectral Based Testing of the Martingale Hypothesis (April 1992). NBER Working Paper No. t0090, Available at SSRN: https://ssrn.com/abstract=994519

Steven N. Durlauf (Contact Author)

University of Chicago ( email )

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National Bureau of Economic Research (NBER)

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Korea Development Institute (KDI) ( email )

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