The Impact of Wavelet Coefficient Correlations on Fractionally Differenced Process Estimation

The discrete wavelet transform (DWT) approximately decorrelates a fractionally di erenced (FD) process, allowing for simple maximum likelihood estimation of the FD process parameters using the wavelet coeÆcients. In previous work we have established limit theorems for the parameters based on a model where scales are uncorrelated and two simple models for withinscale correlation, namely, white noise and a rst order autoregressive (AR) process. Here we assess the adequacy of these simple models for handling betweenand within-scale correlations. We compare the performance of these simple models for estimating the FD process parameters against procedures that use longer wavelet lters (to reduce between-scale correlations) and use AR models of higher order (to more precisely model within-scale correlations).