OLS Estimate of Fractional Differencing Parameter Using Wavelets Derived from Smoothing Kernels

Mark Jensen

Econometrics from University Library of Munich, Germany

Abstract: This paper develops a consistent OLS estimate of a fractionally integrated processes' differencing parameter, using continuous wavelet theory as constructed from smoothing kernels. We show that a log-log linear relationship exists between the variance of the wavelet coefficient and the level at which the fractionally integrated processes is smoothed. This linear relationship occurs because the self-simularity property of the fractionally integrated process and the self-similarity of the wavelet causes the smoothing level to continually appear in the wavelet transformation. Since the wavelet coefficient can be interpreted as the k-th order details of the series at some level of smoothing, we also show that the above log-log relationship can be derived from the variance of the 1-st order derivative of the time series smoothed by a kernel that is well localized in both time and frequency space. Lastly, we derive the asymptotic biasness and variance of the OLS estimate and test our consistent estimate with a number of Monte Carlo experiments.

Keywords: Fractionally Integrated Processes; Long-Memory; Smoothing Kernels; Wavelets (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Pages: 25 pages
Date: 1995-06-07
Note: 25 pages, written in an implementation of TeX; binary PostScript file was FTP'ed. There are several figures so PostScript file is large (3.27Mb)
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:9506002

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