Application Research Of Optimization Theory And Wavelet Analysis In Time Series Analysis

Time series analysis is a vigorous branch in statistics, it studies the variation law and characteristics of time series by modern statistics and information processing technology,and predict the future trend of the time series. In order to improve the forecasting accuracy,we need to fit an appropriate time series model better, so we should put forward a more effective parameter estimate method of time series model. Proceeding from this point, this paper presents two optimization methods of parameter estimate method of time series model to make the fitting effect of the model remarkable. Because of the time series often have nonlinear and high noise, especially stock sequence, this demands suitable model to raise forecast accuracy. To solve this problem, we introduce combination method based on the wavelet theory and artificial neural network model to analysis and predict the stock sequence.In this paper, the parameters of the time series model are estimated by using the conjugate gradient method and the spectral conjugate gradient method, and we pretreat the time series by using wavelet transform theory, then using the neural network to model and forecast the de-noising series.First, this paper introduces research background, purpose, significance and research status, gives the research principle of the conjugate gradient method and the spectral conjugate gradient method, and summarizes the research and development of the wavelet analysis and neural network.Secondly, we introduce two important model for time series: ARMA model and ARIMA model, and systematically demonstrate the optimization method of parameter estimation methods for time series analysis model, and depth study the basic media of the conjugate gradient method and spectral conjugate gradient method. On the basis of the given theory, the problem of parameter estimation of time series model is transformed into an unconstrained optimization problem. In the third chapter of the paper, we construct a new hybrid conjugate gradient method based on the existing literature. In the fourth chapter, a new spectral conjugate gradient method is proposed. We use the test functions to verify the new methods, and the numerical results show that the algorithms are effective.The application of the two methods for time series show that they can fit the model parameters.Thirdly, we introduce the theory of wavelet analysis and wavelet de-noising, and research the wavelet threshold de-noising algorithm, then put forward a new threshold function and a new threshold, and make simulation experiment for three noise signal. The simulation figure and numerical result show that the algorithm is effective, and prove that the wavelet analysis can be used to de-noising research for non-stationary time series.Lastly, we summarize the artificial neural network and its relevant theories, and discuss Elman neural network model in detail, and then put forward a method combine the wavelet de-noising method with Elman neural network model. At first, the de-noising pretreatment is carried out for the Shanghai composite index closing price. And then we apply Elman neural network to model and forecast the series. Compared with other methods, the forecasting effect is good.