A Wavelet Solution to the Spurious Regression of Fractionally Differenced Processes

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. ∗I started working on this paper when I was at University of Windsor; Financial supports from the Natural Sciences and Engineering Research Council of Canada and the Social Sciences and Humanities Research Council of Canada are gratefully acknowledged. †The author gratefully acknowledges support from the National Science Foundation under Grants DMS9815344 and DMS93-12686 for the Geophysical Statistics Project and its research.