P-Value Approximation For The Log-Likelihood Ratio Statistic To Vector Autoregression


Chia-Hao Chang
2010-06-18  10:00 - 12:00
Room 504, Freshman Classroom Building

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 are 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 (1998) to find a representation for the p-value approximation as a → ∞.