Wavelet estimation of a local long memory parameter

Abstract

There are a number of estimators of a long-memory process' long-memory parameter when the parameter is assumed to hold constant over the entire data set, but currently no estimator exists for a time-varying long-memory parameter. In this paper we construct an estimator of the time-varying long-memory parameter that is based on the time-scale properties of the wavelet transform. Because wavelets are localised in time they are able to capture the time-varying statistical properties of a locally stationary longmemory process, and since wavelets are also localised in scale they identify the self-similarity scaling behaviour found in the statistical properties of the process. Together the time and scale properties of the wavelet produce an approximate log-linear relationship between the time-varying variance of the wavelet coefficients and the wavelet scale proportional to the local long-memory parameter. To obtain a least-squares estimate of the local long-memory parameter, we replace the ...

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