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 main tasks to research them is how to estimate corresponding series parameters. There exist some current methods, such as the Traditional maximum likelihood estimation (TMLE) and Least square estimation (LSE) etc., but the huge computation burden is always a bottleneck to utilize them broadly in many applications. To overcome this difficulty, two new parameter estimation method, named identically Multiscale maximum likelihood estimation (MMLE), are proposed by combining Discrete wavelet transform (DWT) and Discrete wavelet package transform (DWPT) with the TMLE in this paper, respectively. These primary ideas are all as follows, firstly, applying the DWT/DWPT to these time series, which possess of some good properties, such as orthogonal decomposition and decorrelation; secondly, analyzing the time series in a multiscale domain, and studying their statistical properties in different scale, such as mean, variance and covariance. These new algorithms can effectively decrease computation complexity and obtain satisfying estimation precision illustrated by the data analysis and computer simulation.