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A wavelet solution to the spurious regression of fractionally differenced processes

SUMMARY 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.