M,-dimensional Ar (p) Model Statistical Diagnostics

In recent years, time series become an important research field in the statistical. Because the model is useful in many problems, such as agriculture, engineering, medicine, meteorology, quality control, sociology and so on, the research of time series model has attracted considerable attention. In fact, the data of time series often includes several variables, in other words, the time series model what we often meet is high dimensional model. For example, sale volume, price, sale force and advertising spending are always involved in variable. So it's worthy of the analysis for high dimensional time series model. Because auto regression model, moving average model and ARMA model can be transformed into auto regression in certain conditions, it's very significant of the statistical analysis for auto regression model.As the major influence analysis models, the data deletion model and the mean shift model are not only adapt to linear regression model, but also the other more complex models. As the basic statistical diagnostic model, the data deletion model is the description of the difference after the deletion of data in the estimation, which means the model analysis the outliers and influential point by deletion of data, mean shift model test the outliers and influential point by anglicizing whether the mean has been drift.In this paper, we introduce the estimation of parameter and its hypothesis testing in m dimensional AR (1) models at first. Then we discuss statistical diagnostics for the model and get the concise Cook statistics based on case deletion model, the equivalency between the case deletion model and the case mean shift outlier model is presented. At last, we obtain the concise Cook statistics of m dimensional AR(p) models, then with the generalized Cook distance, the W-K statistics and AP statistics are obtained.