OLS Estimate of Fractional Differencing Parameter Using Wavelets Derived from Smoothing KernelsEconometrics from EconWPA 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) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpem:9506002 Access Statistics for this paper More papers in Econometrics from EconWPA |
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