Time-Varying Long Memory Parameter Estimation Based on Wavelets

Stationary long memory process has beenwidely studied in the literature. In this article, we considered thelocally stationary long memory process with time-varying memoryparameter. A new wavelet-based algorithm was developed usinglog-linear relationship between the wavelet coefficient variance andthe scaling parameter. The consistency and the finite samplebehavior of the estimator have also been studied, which provide agood reference for the practitioner and researchers. The newalgorithm has also been applied to the YEN/USD exchange rate series,which leads to some interesting results.