The Autoregressive Model Of Total Least Square Analysis

Time series uses stochastic process theory and mathematical statistic method tostudy the law of the sequence of random data. The AR model is one of the three types oftime series models and is the most common model of time series models.The core elementis the determination of modeling parameters and ordering the Model. At present, LS is thebest way to estimate the algorithm of time series model parameter estimations. Model isbased on variable of itself or other related variables changed in the past to predict futurechanges. So each variable is the dependent variable and independent variable when solvingthe problems. We get each quantity through some measuring methods, so it is inevitableto have errors. While solving parameters through LS is to assume there is nor error orcoefficient matrix consider arrays of the coefficient of error, and only to consider thecurrent observations of the error. Obviously,this model must have deviation. So this textwill introduce a new parameters estimation method, i.e. TLS, to solve the parametervaluations. This method considers the independent variable and dependent variable existthe error in the process of solving problems.This paper first discusses the research background, and the research situation ofregression AR model and the overall least square; Second discusses the detais in regressionAR model parameters, the commonly use method of the basic theory (this article mainlyuse the least squares solution of the parameters),the model to determine order number, andits usage scope; Moreover, it discusses the basic principles of integrated least squares, theapplication of a unitary linear regression model and multivariate linear regressionmodel.We draw the conclusion through the solution of the example analysis.On the basis offormer two parts,we discuss and classify the regression AR model, then conclude therelation of the two kinds of models, linear regression model and a multiple linearregression model.Thus we deduce the solution method and the steps of the parameters ofoverall least squares, and give analysis through the examples; Finally, we summarize themain content and conclusions of this paper, and what still need to be further discussed.