Researches On The Multi-Scale Time Series Analysis

As one of the branches of statistics, time series analysis focuses on the variation characters and trend of discrete ordered data series mainly. For a long time, time series analysis has been applying in many fields successfully, such as economics, finance, management, chronometer, aerography, oceanography, physical geography, biology, iatrology, mechanics, electronic engineering etc. So the exploration of the theories and methods of time series has always been a hot research topic. The main methods of time series analysis consist of time domain methods and frequency domain methods. However, without the perfect time-frequency quality, most of these methods usually can not do some multi-scale analysis.In nature and engineering practices, many phenomena or processes have the multi-scale characters or multi-scale effects. While people often observe or measure phenomena and processes at different scales. So it is natural to describe and analysis these phenomena and processes according to multi-scale system theory which can show the essence of these phenomena and processes appropriately. Besides, as a time-frequency method, multi-scale analysis can solve many practical problems in a conceit way with the low computation complexity.Applying the multi-scale analysis into time series analysis is the so-called multi-scale time series analysis. In the multi-scale framework, this thesis has developed and researched several basic problems and methods of time series analysis, that is, the analysis of second-order moment, maximum likelihood estimation of process parameters and the real-time dynamic forecasting of time series, which enrich the traditional analysis methods of time series. The main contributions of this thesis are as follows:1. The multi-scale variance reflects the variability of time series at scales, and provides a base upon which information about two-order moment can be abstracted in a multi-scale framework. In this thesis, the basic property of the...