Wavelet-based estimation of the long memory parameter in Gaussian
non-gappy and gappy time series.
Peter F. Craigmile, Ph.D.
Department of Statistics
The Ohio State University, Columbus, Ohio
Knowledge of the long range dependence (LRD) parameter is critical to
studies of fractal and self-similar behavior. However, statistical
estimation of the LRD parameter becomes difficult when observed data
are masked by short range dependence and other noise, or are gappy in
nature (i.e., some values are missing in an otherwise regular sampling).
After providing a review of LRD, we investigate estimation of the LRD
parameter for Gaussian time series based upon wavelet variances.
In the non-gappy case, our least-squares-based approach extends and
improves upon existing methods by incorporating correlations between
wavelet scales. For the more difficult gappy case, we also develop
estimation methods by using novel estimators of the wavelet variances.
We consider two applications; one for gappy Arctic sea-ice draft data,
and another for non-gappy and gappy daily average temperature data
collected at 17 locations in south central Sweden.
This research project is joint with Debashis Mondal, Ph.D., from the
Department of Statistics, Oregon State University.