檢測向量自我迴歸模型下概似比的 p-value 估計

Abstract

We are interested in the probability that the maximal value of a stochastic process exceeds a value a. The change-point detection is an example. A p-value approximation is obtained as a is large enough for testing a null hypothesis that all observations from the standard normal distribution are independent on the multi-dimensional index set against an alternative that they have a specific form on a particular subregion of the multi-dimensional index set, which is assigned to a vector autoregressive model in this paper. The VAR model is a natural extension of the univariate autoregressive model when multiple time series is concerned. Many methods have been developed to approximate the tail probabilities of the distribution of the maximum under null hypothesis. We use the method introduced by Yakir and Pollak to find a representation for the p-value approximation as a is large.