Spectral Based Testing of the Martingale Hypothesis
AbstractThis 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.
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Bibliographic InfoPaper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0090.
Date of creation: Apr 1992
Date of revision:
Publication status: published as Journal of Econometrics, Vol. 50, No. 3, pp. 355-376, (1991).
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Other versions of this item:
- Durlauf, Steven N., 1991. "Spectral based testing of the martingale hypothesis," Journal of Econometrics, Elsevier, vol. 50(3), pages 355-376, December.
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