Title
Wavelet Based Estimation for Trend Contaminated Long Memory Processes
Speaker
Peter Craigmile, Department of Statistics, University of Washington, Seattle
Abstract
A common problem in the analysis of environmental time series is how to deal with a possible trend component, which is usually thought of as large scale (or low frequency) variations or patterns in the series that might be best modelled separately from the rest of the series. Trend is often confounded with low frequency stochastic fluctuations, particularly in the case of models such as fractionally differenced (FD) processes, which can account for long memory dependence (slowly decaying auto-correlation) and can be extended to encompass non-stationary processes exhibiting quite significant low frequency components. In this talk we assume a model of polynomial trend plus FD noise and apply the discrete wavelet transform (DWT) to separate a time series into pieces that can be used to estimate both the FD process parameters and the trend. The estimation of the process parameters is based on an approximative maximum likelihood approach that is made possible by the fact that the DWT decorrelates FD process approximately. Once the parameters have been estimated, we can then test for a non-zero trend. We demonstrate our methodology by applying it to the analysis of a paleoclimatic time series from the Seychelles.
