The Research And Application Of Time Series Analysis

Time series analysis is the important approach to solve and analyze the dynamic data. It is actual value to applied research study, which is basic on the probability statistics to analyze random data series (or called dynamic data series), develop the mathematic model, and further apply to forecast, adaptive control, and so on.With the development of the method of time series analysis, the applied field is more and more wide, thus the precision of the model is required to higher level. Various method of parameter estimation is come down to solve the optimization problem of the highly nonlinear function, and the confidence about parameter estimation by the traditional optimization approach is lower, therefore, in the paper, the complex optimization problem is solved by applying genetic algorithm (GA) to the parameter estimation of the time series model. GA which is an universal algorithm is more advantageous than the traditional optimization approach when the optimization problem of the highly nonlinear function is achieved. But this algorithm exists some limitation in practice, which appears the phenomena of the prematurity, the bad capability to obtain the local solution of the optimization problem and the slowly converge rate, and so on.. Hence the modified method of GA when we estimate parameters of the time series model by GA is provided.In this thesis four aspects are studied. Firstly, illustrate the background and the meaning to analyze the time series, and provide the research actuality of the development and the approach of parameter estimation. Secondly, analyze the theory method of modeling the time series analysis. Thirdly, illustrate the research actuality of the development and the approach of GA and capture the theory and the operator flow of improved real coding based genetic algorithm (IRGA). The last one, according to the theory of the time series analysis and GA, the GA is introduced in the process of modeling the time series, which is discussed and studied. The following conclusions are achieved:1. The concepts of time series and the related concepts are provided. It is analyzed which is the characteristics of time series , the research tool and the eigenfunction of time series. ARIMA model system is analyzed and discussed. The usual approach of fitting of model parameter estimation is introduced and the limitation of parameter estimation is probed. The theory and the flow of the Box-Jenkins modeling are introduced, and the theory method of the linear minimum variance forecast is introduced. 2. GA is illustrated in this paper, some are also simple introduced, thus the components, algorithm flow and the realization of simple genetic algothm (SGA). Contemporarily, the research development and the characteristics of RGA are illustrated and selection operator, crossover operator,mutation operator and fitness function of RGA is captured. The principle and the algorithm flow of IRGA are provided.3. By the demonstration, the precision of SGA and IRGA, which are respectively applied to the parameter estimation of the time series model, are contrasted with the precision of the approach of the traditional time series analysis. In the end, the conclusion is achieved. In the case of the selected error index, the fitting of precision of the time series model, which is obtained by the parameter estimation used IRGA, is the highest.4. the research result is applied on modeling and forecasting time series about the electric power system load. The applicability is tested and the forecast effect is obtained.