This paper is concerned with tests for seasonal unit roots in a univariate time series process. We construct test statistics which are similar, both exactly and asymptotically, with respect to both the initial values of the process and the possibility of differential seasonal dirft under the...

In this paper we consider the problem of testing the null hypothesis that a series has a constant level against the alternative that the level follows a random walk. This problem has previously been studied by inter alia, Nyblom and Makelainen in the context of the orthogonal random walk plus...

In this paper, we analyse the behaviour of regression-based tests for seasonal unit roots when the error is periodically heteroscedastic. We show, using the case of quaterly data to illustrate, that the limiting null distribution of tests for unit roots at the zero and Nyquist frequencies are...

The contribution of this paper is three-fold. Firslty, a characterisation of the sub-hypotheses comprising the seasonal unit root hypothesis is presented which provides a precise formulation of the alternative hypotheses against which regression-based seasonal unit root tests test. Secondly, it...

This paper builds upon the existing literature on tests of the full hypothesis of deterministic seasonality in a univariate time-series process against the alternative of unit root behaviour at some or all of the zero and seasonal frequencies. Under the assumption of independent Gaussian errors...

In this paper the author uses numerical techniques to investigate the finite sample porperties of data-based approaches to selecting the lag truncation order in the context of the augmented Dickey-Fuller unit root test in a general autoregressice first-order integrated moving-average model.

This paper considers the problem of testing for a nonstochastic seasonal unit root in a seasonally observed time-series process against the alternative of a randomized seasonel root with mean unity; that is, the process displays heteroscedastic seasonal integration.