Study on Multiscale Least Squares and Application in Parameter Identification

In various theoretical research and engineering, the long memory processes are widely found and studied in many applications. Maximum likelihood estimation is usually used to capture the relevant parameters, but it can't be utilized broadly because of the huge burden of computability. In this paper, we firstly use discrete wavelet transform to analyze stochastic processes of time series scale-by-scale, then study the variance and statistical properties of the series over a range of different scales. Subsequently, apply least squares estimation to parameter estimation according to the property that log variance is approximately simple linear equation of log scale, finally a new method named multiscale least squares estimation is put forward. The new algorithm can effectively decrease computation complexity and obtain satisfying estimation precision. This advantage is validated by the data analysis and computer simulation