Two-dimensional Ar (1) Model And Ma (1) Error Linear Model Statistical Diagnostics

Time series analysis useful in many problems especially for econometric and social science applications, become an important research field in the probability statistical. This paper present the two Dimensional AR(1) models and linear regression models with MA(1) errors. The estimation of two Dimensional AR(1) models parameters is given at first. Then,we get the concise diagnostic expression based on case deletion model, establish an equivalence between the case mean shift outlier model form which we derive tests for outliers. Numerical examples are given to illustrate our results. We also give the estimation of parameters in linear regression models with MA(1) errors. Then, we give test statistic from the test for correlation and heteroscedasticity.At last we introduce the statistical diagnostics based on case deleted models.