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A Consistent Test for the Martingale Difference Assumption

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  • Ignacio N. Lobato

    (Instituto Tecnologico Autonomo de Mexico)

Abstract

This paper considers testing that an economic time series follows a martingale difference process. The martingale difference hypothesis has been typically tested using information contained in the second moments of a process, that is, using test statistics based on the sample autocovariances or in the periodograms. Tests based on these statistics are inconsistent since they just test necessary conditions of the null hypothesis. In this paper we consider tests that are consistent against all fixed alternatives and against Pitman's local alternatives. Since the asymptotic distributions of the tests statistics depend on the data generating process, the tests are implemented using a modification of the wild bootstrap procedure. The paper justifies theoretically the proposed tests and examines their finite sample behavior by means of Monte Carlo experiments. In addition we include an application to exchange rate data.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0278.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0278

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  8. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Working Papers, University of Iowa, Department of Economics 99-02, University of Iowa, Department of Economics.
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  22. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An adaptive, rate-optimal test of a parametric model against a nonparametric alternative," SFB 373 Discussion Papers 1999,10, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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