Bayesian Inference in Cointegrated I (2) Systems: a Generalisation of the Triangular Model

This paper generalises the cointegrating model of Phillips (1991) to allow for I (0) , I (1) and I (2) processes. The model has a simple form that permits a wider range of I (2) processes than are usually considered, including a more flexible form of polynomial cointegration. Further, the specification relaxes restrictions identified by Phillips (1991) on the I (1) and I (2) cointegrating vectors and restrictions on how the stochastic trends enter the system. To date there has been little work on Bayesian I (2) analysis and so this paper attempts to address this gap in the literature. A method of Bayesian inference in potentially I (2) processes is presented with application to Australian money demand using a Jeffreys prior and a shrinkage prior.

Bayesian forecasting using stochastic search variable selection in a VAR subject to breaks

This paper builds a model which has two extensions over a standard VAR. The …rst of these is stochastic search variable selection, which is an automatic model selection device which allows for coefficients in a possibly over-parameterized VAR to be set to zero. The second allows for an unknown number of structual breaks in the VAR parameters. We investigate the in-sample and forecasting performance of our model in an application involving a commonly-used US macro-economic data set. We …nd that, in-sample, these extensions clearly are warranted. In a recursive forecasting exercise, we …nd moderate improvements over a standard VAR, although most of these improvements are due to the use of stochastic search variable selection rather than the inclusion of breaks

Efficient posterior simulation in cointegration models with priors on the cointegration space

A message coming out of the recent Bayesian literature on cointegration is that it is important to elicit a prior on the space spanned by the cointegrating vectors (as opposed to a particular identi…ed choice for these vectors). In this note, we discuss a sensible way of eliciting such a prior. Furthermore, we develop a collapsed Gibbs sampling algorithm to carry out e¢ cient posterior simulation in cointegration models. The computational advantages of our algorithm are most pronounced with our model, since the form of our prior precludes simple posterior simulation using conventional methods (e.g. a Gibbs sampler involves non-standard posterior conditionals). However, the theory we draw upon implies our algorithm will be more e¢ cient even than the posterior simulation methods which are used with identi…ed versions of cointegration models

Bayesian inference in a cointegrating panel data model

This paper develops methods of Bayesian inference in a cointegrating panel data model. This model involves each cross-sectional unit having a vector error correction representation. It is flexible in the sense that different cross-sectional units can have different cointegration ranks and cointegration spaces. Furthermore, the parameters which characterize short-run dynamics and deterministic components are allowed to vary over cross-sectional units. In addition to a noninformative prior, we introduce an informative prior which allows for information about the likely location of the cointegration space and about the degree of similarity in coefficients in different cross-sectional units. A collapsed Gibbs sampling algorithm is developed which allows for efficient posterior inference. Our methods are illustrated using real and artificial data

Bayesian inference in the time varying cointegration model

There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved Vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper we develop time varying parameter models which permit coin- tegration. Time-varying parameter VARs (TVP-VARs) typically use state space representations to model the evolution of parameters. In this paper, we show that it is not sensible to use straightforward extensions of TVP-VARs when allowing for cointegration. Instead we develop a speci…cation which allows for the cointegrating space to evolve over time in a manner comparable to the random walk variation used with TVP-VARs. The properties of our approach are investigated before developing a method of posterior simulation. We use our methods in an empirical investigation involving a permanent/transitory variance decomposition for inflation

The effect of the Earth's oblate spheroid shape on the accuracy of a time-of-arrival lightning ground strike locating system

The algorithm used in previous technology time-of-arrival lightning mapping systems was based on the assumption that the earth is a perfect spheroid. These systems yield highly-accurate lightning locations, which is their major strength. However, extensive analysis of tower strike data has revealed occasionally significant (one to two kilometer) systematic offset errors which are not explained by the usual error sources. It was determined that these systematic errors reduce dramatically (in some cases) when the oblate shape of the earth is taken into account. The oblate spheroid correction algorithm and a case example is presented

On the evolution of monetary policy

This paper investigates the evolution of monetary policy in the U.S. using a standard set of macroeconomic variables. Many recent papers have addressed the issue of whether the monetary transmission mechanism has changed (e.g. due to the Fed taking a more aggressive stance against in‡ation) or whether apparent changes are simply due to changes in the volatility of exogenous shocks. A subsidiary question is whether any such changes have been gradual or abrupt. In this paper, we shed light on these issues using a mixture innovation model which extends the class of time varying Vector Autoregressive models with stochastic volatility which have been used in the past. The advantage of our extension is that it allows us to estimate whether, where, when and how parameter change is occurring (as opposed to assuming a particular form of parameter change). Our empirical results strongly indicate that the transmission mechanism, the volatility of exogenous shocks and the correlations between exogenous shocks are all changing (albeit at different times and to di¤erent extents) Furthermore, evolution of parameters is gradual