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A wavelet solution to the spurious regression of fractionally differenced processes

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  • Yanqin Fan
  • Brandon Whitcher

Abstract

In this paper we propose to overcome the problem of spurious regression between fractionally differenced processes by applying the discrete wavelet transform (DWT) to both processes and then estimating the regression in the wavelet domain. The DWT is known to approximately decorrelate heavily autocorrelated processes and, unlike applying a first difference filter, involves a recursive two‐step filtering and downsampling procedure. We prove the asymptotic normality of the proposed estimator and demonstrate via simulation its efficacy in finite samples. Copyright © 2003 John Wiley & Sons, Ltd.

Suggested Citation

  • Yanqin Fan & Brandon Whitcher, 2003. "A wavelet solution to the spurious regression of fractionally differenced processes," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 19(3), pages 171-183, July.
    • Handle: RePEc:wly:apsmbi:v:19:y:2003:i:3:p:171-183
    DOI: 10.1002/asmb.497
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    Cited by:

    1. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
    2. Baruník, Jozef & Hlínková, Michaela, 2016. "Revisiting the long memory dynamics of the implied–realized volatility relationship: New evidence from the wavelet regression," Economic Modelling, Elsevier, vol. 54(C), pages 503-514.
    3. Barunik, Jozef & Barunikova, Michaela, 2015. "Revisiting the long memory dynamics of implied-realized volatility relation: A new evidence from wavelet band spectrum regression," FinMaP-Working Papers 43, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.

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