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Spectral based testing of the martingale hypothesis

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  • Durlauf, Steven N.

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

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 50 (1991)
Issue (Month): 3 (December)
Pages: 355-376

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Handle: RePEc:eee:econom:v:50:y:1991:i:3:p:355-376

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Mankiw, N. Gregory & Campbell, John, 1987. "Permanent and Transitory Components in Macroeconomic Fluctuations," Scholarly Articles 3207697, Harvard University Department of Economics.
  2. Adrian R. Pagan & G. William Schwert, 1990. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
  3. 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.
  4. David S. Bizer & Steven N. Durlauf, 1990. "Testing the Positive Theory of Government Finance," NBER Working Papers 3349, National Bureau of Economic Research, Inc.
  5. Robert J. Barro, 1981. "On the Predictability of Tax-Rate Changes," NBER Working Papers 0636, National Bureau of Economic Research, Inc.
  6. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
  7. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  8. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
  9. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
  10. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
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