Optimization Of Autoregressive Model For Time Series With Trend Term

In the research and analysis of time series,it can be found that the observed data often have some unknown trend similar to increasing or decreasing,and there are still some unobservable residuals.The traditional autoregressive model is more suitable for linear conditions,and requires a higher degree of stability for the time series.However the data observed in real life,especially in finan-cial time series analysis,such as stocks,futures and other trade and financial data is difficult to have a clear regularity.And the data usually is nonlinear and nonstation ary.The problem studied in this paper is to introduce the idea of local regression and moving average in the model to fit data with nonlinear characteristics.The observed data has a certain trend,but it doesnt have to be a simple linear trend,so this article introduces the idea of local regression to fit the trend item of the data first,and then estimates the residual by autoregression.First,,we introduce the Hurst index that can be used to distinguish the nonlinearity and memory of the sequence and the R/S analysis method to calculate this index.Accordingly determine whether the sequence needs to be estimated using the model introduced in this article.This article assumes that the model is composed of a certain trend term and an error term.Based on the existing method that the trend term is estimated by the local weighted linear regression estimation and the error term is estimated by the autoregression(AR)model,the concept of average field is introduced.An optimized time series fitting model is proposed,which is to estimate the trend term by using local weighted linear regression after moving average processing.The model analysis effects of different window widths and differentautoregressive coefficients are discussed.This article uses this step of moving average processing to preliminary denoise the data and neutralize the interference of the autoregressive part on the estimation of trend items.The data.simulation results show that this method obviously optimizes the estimation effect for some forms of data.To enhance the applicability of the model,this paper brings in a function coef-ficient autoregressive model to estimate the trend term.Thereinto,the coefficient function uses local weighted linear smoothing technology to estimate.This model is constructed from the data itself and has more flexibility.In order to select the optimal bandwidth and determine the dependent variables of the model,a non-parametric APE criterion is proposed.However,data simulation shows that this model combined with the AR model will have an over-fitting situation.When the order is relatively large,the efficiency of the model is relatively low,and the calculation is more complicated.Therefore,we try to disassemble the model,the trend item is selected as the overall trend item estimate,and then the residual error autoregressive fitting is performed.Through the simulation studies,it is found that,this model has wider application range and better fitting effect.