Publication at Faculty of Mathematics and Physics |
2011
Abstract
In this paper we study asymptotic properties of an efficient score statistic for testing changes in the parameter values of an autoregressive time series. We assume that the error process is a martingale difference sequence with known variance instead of independent identically distributed (i.i.d.) random variables.
The procedure allows testing changes in the mean and in the autoregressive parameters separately. We present the invariance principle and the law of the iterated logarithm for martingale difference sequences and linear processes, and show that the asymptotic distribution of statistics under consideration is the same as in the case of i.i.d. errors.