Research On Functional Variable-coefficient Auto-regression Forecast Method For Time Sequence

Time series forecast is used to study the regularity of random data sequence by random process theory and mathematical statistics method.As one of the most common models of time sequence,auto-regressive model has solid theoretical foundation and is widely applied to many fields.Model coefficient is one of the keys for determination of auto-regressive forecast model.Traditional auto-regressive models assume that the regression coefficient is constant,which means that the effect of series for the current moment to the past time is fixed,but it is not entirely true.Aiming at the problem,variable coefficient is optimized by functional smooth technology and then the selection of smooth coefficient is improved.In so doing,the better results of the time series prediction can be obtained.The main research works include:(1)Researches on the estimating coefficient of auto-regressive model.In this process,coefficient's influence is fixed of variable itself for the past to the future,which affects the accuracy of the estimation model.To solve this problem,this thesis proposes the Functional variable-coefficient auto-regression forecast method of time Sequence.The proposed model establish linear equations to the observation value in order to get coefficient matrix,then regression coefficients is obtained in the process of smooth b-spline basis function fitting and smoothing,finally estimated coefficient is composed by linear combination to get predictive value of time series.The experimental results on data sets demonstrate that the proposed model's prediction accuracy is better than that of traditional AR model and ARMA model.(2)Researches on the coefficient matrix functionalizing process.In this process,smoothing coefficient plays a compromising role between weighing loss and the risk of over fitting.Generalized Cross-validation(GCV)is a general and better parameter selection way,but massive calculation may be needed in order to get a more accurate smoothing parameter because GCV is calculated on discrete values.Aiming at this problem,the fitting optimization and the finite difference solution strategy are proposed to improve the solution efficiency of selection of the optimal smoothing coefficient,and their precision and efficiency are compared and analyzed.The experiment results demonstrate that the two proposed strategies are greatly improved in efficiency compared with the conventional grid method with almost the same precision.The finite difference solution strategy is better than the fitting optimization solution strategies in terms of algorithm precision,and then latter is more efficient.This thesis presents the functional variable-coefficient auto-regression forecast model of time sequence and two kinds of optimization strategy for Smooth coefficient.The inherent shortcomings for estimating coefficients of auto-regressive AR model and the prediction accuracy can be improved,and the selection method of smooth coefficient in data fitting is promoted as well.The obtained results have a certain reference significance and application value for application researches of Auto-regressive model forecast and data functionalizing.