P. F. Craigmile, D. B. Percival and P. Guttorp (2000), `The Impact of Wavelet Coefficient Correlations on Fractionally Differenced Process Estimation,' to appear in 3ECM conference proceedings.
The discrete wavelet transform (DWT) approximately decorrelates a fractionally differenced (FD) process, allowing for simple maximum likelihood estimation of the FD process parameters using the wavelet coefficients. In previous work we have established limit theorems for the parameters based on a model where scales are uncorrelated and two simple models for within-scale correlation, namely, white noise and a first order autoregressive (AR) process. Here we assess the adequacy of these simple models for handling between- and within-scale correlations. We compare the performance of these simple models for estimating the FD process parameters against procedures that use longer wavelet filters (to reduce between-scale correlations) and use AR models of higher order (to more precisely model within-scale correlations).
Go to home page for Don Percival