Time Series Model Of Local Influence

Time series analysis becomes an important research field in the mathematical statistics for the application of econometrics, signal processing and meteorology. In the past two decades, there are lots of theories in the parameter estimation, determination of the order and the application,a number of authors have been concerned about the diagnostics of models with dependent errors. Due to the complicated dependence structure in the data, the analysis of outliers and influence points in time series become complicated.Local influence analysis is a new method of the influential point identification in recent years. In this paper, we use the local influence to find the outlier and the influential point in AR(1) model, we calculate the curvature the formula of local influence, which helps us to detect all of the influential point at a time, and an example is given to illustrate the effectiveness of the conclusion. Then based on general influence function and Cook statistic, we investigate the local influence small perturbation on the auto covariance function.In ordinary AR(1) models, random errors are assumed to satisfy the Gauss-Markov conditions, however, random errors are had to satisfy the assumption of homogeneous variances in measuring econometric. In this paper, we introduce the estimation of parameters in AR(1)-ARCH(1) models and its test for condition heteroscedasticity, then the curvature formula of the model is calculated with the tech of local influence.