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Spectral Based Testing of the Martingale Hypothesis

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Steven N. Durlauf

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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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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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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(1989-2), pages 69-136. [Downloadable!]
  2. 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. [Downloadable!] (restricted)
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  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  4. Bizer, David S. & Durlauf, Steven N., 1990. "Testing the positive theory of government finance," Journal of Monetary Economics, Elsevier, vol. 26(1), pages 123-141, August. [Downloadable!] (restricted)
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  5. John Y. Campbell & N. Gregory Mankiw, 1987. "Permanent and Transitory Components in Macroeconomic Fluctuations," NBER Working Papers 2169, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
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  7. Robert J. Barro, 1981. "On the Predictability of Tax-Rate Changes," NBER Working Papers 0636, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  8. 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, Oxford University Press for Society for Financial Studies, vol. 1(1), pages 41-66. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  10. Pagan, A.R. & Schwert, G.W., 1989. "Alternative Models For Conditional Stock Volatility," Papers 89-02, Rochester, Business - General.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Carlos Velasco & Ignacio N. Lobato, 2004. "A simple and general test for white noise," Econometric Society 2004 Latin American Meetings 112, Econometric Society. [Downloadable!]
  2. Jon Vilasuso & Steve Cunningham, 1996. "Tests for Nonlinearity in EMS Exchange Rates," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 1(3), pages 155-168. [Downloadable!] (restricted)
  3. Chung-Ming Kuan & Wei-Ming Lee, 2004. "A New Test of the Martingale Difference Hypothesis," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 8(4), pages 1191-1191. [Downloadable!] (restricted)
  4. Juan Carlos Escanciano & Silvia Mayoral, . "Data-Driven Smooth Tests for the Martingale Difference Hypothesis," Faculty Working Papers 01/07, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  5. Jeremy Berkowitz, 1999. "Evaluating the forecasts of risk models," Finance and Economics Discussion Series 1999-11, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  6. Joon Park & Yoon-Jae Whang, 2005. "A Test of the Martingale Hypothesis," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 9(2), pages 1163-1163. [Downloadable!] (restricted)
  7. Choi, In, 1999. "Testing the Random Walk Hypothesis for Real Exchange Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 293-308, May-June. [Downloadable!]
  8. Ignacio N. Lobato, 2000. "A Consistent Test for the Martingale Difference Assumption," Econometric Society World Congress 2000 Contributed Papers 0278, Econometric Society. [Downloadable!]
  9. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2005. "Evaluating Value-at-Risk models with desk-level data," Working Paper Series 010, North Carolina State University, Department of Economics, revised Dec 2006. [Downloadable!]
  10. Luca Bindelli, 2005. "Testing the New Keynesian Phillips curve: a frequency domain approach," Money Macro and Finance (MMF) Research Group Conference 2005 69, Money Macro and Finance Research Group. [Downloadable!]
  11. Jeremy Berkowitz, 1996. "Generalized spectral estimation," Finance and Economics Discussion Series 96-37, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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