http://repub.eur.nl/res/aut/978/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/38803/ 2012-12-01T00:00:00Z http://repub.eur.nl/res/pub/1915/ 2005-03-11T00:00:00Z The purpose of this paper is to survey and critically assess the Bayesian cointegration literature. In one sense, Bayesian analysis of cointegration is straightforward. The researcher can combine the likelihood function with a prior and do Bayesian inference with the resulting posterior. However, interesting and empirically important issues of global and local identification (and, as a result, prior elicitation) arise from the fact that the matrix of long run parameters is potentially of reduced rank. As we shall see, these identification problems can cause serious problems for Bayesian inference. For instance, a common noninformative prior can lead to a posterior distribution which is improper (i.e. is not a valid p.d.f. since it does not integrate to one) thus precluding valid statistical inference. This issue was brought forward by Kleibergen and Van Dijk (1994, 1998). The development of the Bayesian cointegration literature reflects an increasing awareness of these issues and this paper is organized to reflect this development. In particular, we begin by discussing early work, based on VAR or Vector Moving Average (VMA) representations which ignored these issues. We then proceed to a discussion of work based on the ECM representation, beginning with a simple specification using the linear normalization and normal priors before moving onto the recent literature which develops methods for sensible treatment of the identification issues. http://repub.eur.nl/res/pub/11332/ 2000-01-01T00:00:00Z In this paper, we make use of state space models to investigate the presence of stochastic trends in economic time series. A model is specified where such a trend can enter either in the autoregressive representation or in a separate state equation. Tests based on the former are analogous to Dickey–Fuller tests of unit roots, while the latter are analogous to KPSS tests of trend stationarity. We use Bayesian methods to survey the properties of the likelihood function in such models and to calculate posterior odds ratios comparing models with and without stochastic trends. We extend these ideas to the problem of testing for integration at seasonal frequencies and show how our techniques can be used to carry out Bayesian variants of either the HEGY or Canova–Hansen test. Stochastic integration rules, based on Markov Chain Monte Carlo, as well as deterministic integration rules are used. Strengths and weaknesses of each approach are indicated. http://repub.eur.nl/res/pub/1603/ 1999-10-13T00:00:00Z In this paper, we make use of state space models to investigate the presence of stochastic trends in economic time series. A model is specified where such a trend can enter either in the autoregressive representation or in a separate state equation. Tests based on the former are analogous to Dickey-Fuller tests of unit roots, while the latter are analogous to KPSS tests of trend-stationarity. We use Bayesian methods to survey the properties of the likelihood function in such models and to calculate posterior odds ratios comparing models with and without stochastic trends. We extend these ideas to the problem of testing for integration at seasonal frequencies and show how our techniques can be used to carry out Bayesian variants of either the HEGY or Canova-Hansen test. Stochastic integration rules, based on Markov Chain Monte Carlo, as well as deterministic integration rules are used. Strengths and weaknesses of each approach are indicated. http://repub.eur.nl/res/pub/2143/ 1998-01-01T00:00:00Z In this paper we analyze the sensitivity of unit root inference to nonlinear transformations through Bayesian techniques. We make joint inference about the Box-Cox transformation, which includes the cases yt and log(yt), and the unit root. When we apply our method to the 14 Nelson-Plosser series, we find that unit root inference can be very sensitive to the transformation chosen and that the usual practice of taking logs is not always warranted. http://repub.eur.nl/res/pub/7799/ 1997-05-08T00:00:00Z In this paper, we make use of state space models to investigate the presence of stochastic trends in economic time series. A model is specified where such a trend can enter either in the autoregressive representation or in a separate state equation. Tests based on the former are analogous to Dickey-Fuller tests of unit roots, while the latter are analogous to KPSS tests of trend-stationarity. We use Bayesian methods to survey the properties of the likelihood function in such models and to calculate posterior odds ratios comparing models with and without stochastic trends. In addition, we extend these ideas to the problem of testing for integration at seasonal frequencies and show how techniques can be used to carry out Bayesian variants of HEGY test or the Canova-Hansen test. http://repub.eur.nl/res/pub/2103/ 1997-01-01T00:00:00Z Recent empirical research into the seasonal and trend properties of macroeconomic time series using periodic models has resulted in strong evidence in favour of periodic integration (PI). PI implies that the differencing filter necessary to remove a stochastic trend varies across seasons and, hence, that seasonal fluctuations are related to the stochastic trend. Previous studies finding evidence of PI have used classical econometric techniques. In this paper, we investigate the possible sensitivity of this empirical result by using Bayesian techniques. An application of posterior odds analysis and highest posterior density interval tests to several quarterly UK macroeconomic series suggests strong evidence for PI, even when we allow for structural breaks in the deterministic seasonals. A predictive exercise indicates that PI usually outperforms other competing models in terms of out-of-sample forecasting