Wavelet transform for regression estimation of non-stationary fractional time series

We consider a semiparametric log periodogram regression estimation of memory parameter $d$ for non-stationary fractional time series using wavelet transformation. We propose wavelet-based log periodogram regression estimator, and obtain the asymptotic mean squared error, consistency and asymptotic normality of the estimator. The convergence rate of the mean squared error is the same as in the stationary case. Simulation studies show that wavelet-based estimator works reasonably well without using data differencing or data tapering, particularly when the short-run dependence is strong