This paper presents exact recursions for calculating the mean and mean square error matrix of the state vector given the observations for the multi-variate linear Gaussian state-space model in the case where the initial state vector is (partially) diffuse. Copyright 2003 Blackwell Publishing Ltd.

Recently, Vogelsang (1999) proposed a method to detect outliers which explicitly imposes the null hypothesis of a unit root. It works in an iterative fashion to select multiple outlier in a given series. We show, via simulations, that, under the null hypothesis of no outliers, it has the right...

The multi-variate t distribution provides a viable framework for modelling volatile time-series data; it includes the multi-variate Cauchy and normal distributions as special cases. For multi-variate t autoregressive models, we study the nature of the innovation distribution and the prediction...

In this paper, we suggest a new set of regression-based statistics for testing the seasonal unit root null hypothesis. These tests are based on combining conventional Hylleberg et al. (1990) -type seasonal unit root test statistics calculated from both forward and reverse estimation of the...

The objective of this paper is to develop default priors when the parameter of interest is the autocorrelation coefficient in normal regression models with first-order autoregressive residuals. Jeffreys' prior as well as reference priors are found. These priors are compared in the light of how...

Let X_k be a stationary time series and y_k=X_kM be the sub-sampled series corresponding to a fixed systematic sampling interval M 1. In this paper, we use a point process approach to study the effect of the sub sampling on the extremal properties of Y_k when X_k is a linear process with...

This paper builds on the existing literature on tests of the null hypothesis of deterministic seasonality in a univariate time-series process. Under the assumption of independent Gaussian errors, we derive the class of locally weighted mean most powerful invariant tests against unit roots at the...

For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite...

In analysing time series of counts, the need to test for the presence of a dependence structure routinely arises. Suitable tests for this purpose are considered in this paper. Their size and power properties are evaluated under various alternatives taken from the class of INARMA processes. We...

We analyse consistent estimation of the memory parameters of a nonstationary fractionally cointegrated vector time series. Assuming that the cointegrating relationship has substantially less memory than the observed series, we show that a multi-variate Gaussian semi-parametric estimate, based on...