We explore the model of the wavelet sequence in each scales when ARFIMA processes are transformed by Daubechies filters. Although the wavelet coefficients of long memory processes are often approximated to uncorrelated sequences within and between scales when we estimate the memory parameter of the processes, there are still some dependence among the coefficients. Especially, Krim and Pesquet (1995) show that the wavelet sequence of ARIMA processes in each scales becomes an ARIMA if the vanishing moments of the wavelet used in analysis is smaller than the order of increments, or an ARMA if not. Using the approach and the results in Krim and Pesquet (1995), we describe the model of wavelet transformed ARFIMA processes. |