The Multiscale Parameter Estimation Methods for a Sort of Time Series

There are a lot of time series in many fields,especially, the long memory time series, and one of maintasks to research them is how to estimate corresponding series parameters. There exist some current methods, suchas the Traditional maximum likelihood estimation (TMLE)and Least square estimation (LSE) etc., but the huge computation burden is always a bottleneck to utilize thembroadly in many applications. To overcome this diffculty,two new parameter estimation method, named identicallyMultiscale maximum likelihood estimation (MMLE), areproposed by combining Discrete wavelet transform (DWT)and Discrete wavelet package transform (DWPT) with theTMLE in this paper, respectively. These primary ideasare all as follows, firstly, applying the DWT/DWPT tothese time series, which possess of some good properties,such as orthogonal decomposition and decorrelation; secondly, analyzing the time series in a multiscale domain, andstudying their statistical properties in different scale, suchas mean, variance and covariance. These new algorithmscan effectively decrease computation complexity and obtain satisfying estimation precision illustrated by the dataanalysis and computer simulation.