Wavelet-Based Estimation for Seasonal Long-Memory Processes

We introduce the multiscale analysis of seasonal persistent processes i e time series models with a singularity in their spectral density function at one or multiple frequencies in The discrete wavelet packet transform DWPT and an non decimated version of it known as the maximal overlap DWPT MODWPT are introduced as an alternative method to spectral techniques for analyzing time series that exhibit seasonal long memory Approximate maximum likelihood estimation is performed by replacing the variance covariancematrix with diagonalized matrix based on the ability of the DWPT to approximately decorrelate a seasonal persistent process Simulations are performed using this wavelet based maximum likelihood technique on a variety of time series models An application of this methodology to atmospheric CO measurements is also presented