It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite...

Asset prices undergo long swings that revolve around benchmark levels. In currency markets, fluctuations involve real exchange rates that are highly persistent and that move in near-parallel fashion with nominal rates. The inability to explain these two regularities with one model has been...

An explication of the key ideas behind the Cointegrated Vector Autoregression Approach. The CVAR approach is related to Haavelmo’s famous “Probability Approach in Econometrics” (1944). It insists on careful stochastic specification as a necessary groundwork for econometric inference and...

This paper gives a systematic application of maximum likelihood inference concerning cointegration vectors in non-stationary vector valued autoregressive time series models with Gaussian errors, where the model includes a constant term and seasonal dummies. The hypothesis of cointegration is...

The cointegrated VAR model is proposed as an empirically coherent framework for analyzing macroeconomic phenomena within a dynamic system of pulling and pushing forces. As an illustration we show how an economic theory for inflation and money demand gives rise to a number of hypotheses...

The purpose of this paper is to give a systematic account of the maximum likelihood inference concerning cointegration vectors in non-stationary vector value autoregressive time series with Gaussian errors. The hypothesis of r cointegration vectors is given a simple parametric formulation in...

This paper discusses a number of likelihood ratio tests on long-run relations and common trends in the I(2) model and provide new results on the test of overidentifying restrictions on β’xt and the asymptotic variance for the stochastic trends parameters, α⊥1: How to specify deterministic...

This paper develops some new tests for structural hypotheses in the framework of a multivariate error correction model with Gausian errors. The tests are constructed by an analysis of the likelihood function and motivated by an empirical investigation of the PPP relation and the UIP relation for...

This paper discusses the I(2) model with breaks in the deterministic component and illustrates the model with an analysis of German and US prices, exchange rates, and interest rates in the period 1975-1999. It provides new results on the likelihood ratio test of overidentifying restrictions on...

It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite...