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A wavelet solution to the spurious regression of fractionally differenced processes
Author(s) -
Fan Yanqin,
Whitcher Brandon
Publication year - 2003
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.497
Subject(s) - spurious relationship , estimator , mathematics , wavelet , regression , autocorrelation , finite impulse response , econometrics , filter (signal processing) , asymptotic distribution , statistics , computer science , algorithm , artificial intelligence , computer vision
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.