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Spectral Based Testing of the Martingale Hypothesis

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  • Steven N. Durlauf

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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0090.

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Date of creation: Apr 1992
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Publication status: published as Journal of Econometrics, Vol. 50, No. 3, pp. 355-376, (1991).
Handle: RePEc:nbr:nberte:0090

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  1. Campbell, John Y & Mankiw, N Gregory, 1987. "Permanent and Transitory Components in Macroeconomic Fluctuations," American Economic Review, American Economic Association, American Economic Association, vol. 77(2), pages 111-17, May.
  2. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, Elsevier, vol. 22(1), pages 27-59, October.
  3. Andrew W. Lo & A. Craig MacKinlay, 1987. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
  4. Bizer, David S. & Durlauf, Steven N., 1990. "Testing the positive theory of government finance," Journal of Monetary Economics, Elsevier, Elsevier, vol. 26(1), pages 123-141, August.
  5. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(5), pages 893-920, October.
  6. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 86(6), pages 971-87, December.
  7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 277-301, March.
  8. Steven N. Durlauf, 1989. "Output Persistence, Economic Structure, and the Choice of Stabilization Policy," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 20(2), pages 69-136.
  9. Adrian R. Pagan & G. William Schwert, 1990. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
  10. Robert J. Barro, 1981. "On the Predictability of Tax-Rate Changes," NBER Working Papers 0636, National Bureau of Economic Research, Inc.
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