When applying Johansen's procedure for determining the cointegrating rank to systems of variables with linear deterministic trends, there are two possible tests to choose from. One test allows for a trend in the cointegration relations and the other one restricts the trend to be orthogonal to...

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized...

In this paper we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling moderate skewness and kurtosis typically encountered in stock return series. The need to allow for skewness can also be readily...

This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. We argue that noncausal autoregressive models are especially well suited for modeling expectations. Unlike conventional causal autoregressive models, they explicitly...

In testing for the cointegrating rank of a vector autoregressive (VAR) process it is important to take into account level shifts that have occurred in the sample period. Therefore the properties of estimators of the time period where a shift has taken place are investigated. The possible...

In applied time series analysis, checking for autocorrelation in a fitted model is a routine diagnostic tool. Therefore it is useful to know the asymptotic and small sample properties of the standard tests for the case when some of the variables are cointegrated. The properties of residual...

A test for the cointegrating rank of a vector autoregressive (VAR) process with a possible shift and broken linear trend is proposed. The break point is assumed to be known. The setup is a VAR process for cointegrated variables. The tests are not likelihood ratio tests but the deterministic...

A small system of German economic variables consisting of the money stock M3, Gross National Product (GNP) and a bond rate is used to illustrate the power of cointegration analysis and the usefulness of some recently developed tools for this kind of analysis. Testing for the cointegrating rank...