Wavelet based Estimation of Time- Varying Long Memory Model with Nonlinear Fractional Integration Parameter

In this paper, we propose a time-varying long memory model where the fractional integration parameter varies nonlinearly according to Smooth Transition Regressive (STR) model. To estimate the fractional integration parameter, we suggest a new estimation method based on wavelet approach. In particular, we consider the instan- taneous least squares estimator (ILSE). We conduct some simulation experiments and provide an empirical application to modeling the dynamics of volatilities of some fi- nancial time series. The obtained results show that the model proposed offers an interesting framework to describe time-varying long range dependence of volatilities and provide evidence of regime change in persistence to shocks.