Limit Theorem for the Maximum of Autoregressive Processes with Uniform Marginal Distributions and Its Implications to the Analysis of Air Pollution Data. Technical Report No. 17

摘要

Limit theorems for maxima of time series are often useful in making statistical inferences in practical problems. In the study of air pollution the peak levels over fixed time periods are of concern. This paper examines a class of models for which the classical theory does not apply. The results indicate that methods like those used in this paper might be necessary to obtain the appropriate limit in some simple stationary models (e.g., first order autoregressive models). Some of these stationary models may be adequate to describe the behavior of some air pollution time series, although the uniform model described in this paper may not. (ERA citation 04:014504)