Tests for the cointegrating rank of a vector autoregressive process are considered which allow for possible exogenous shifts in the mean of the data generation process. The break points are assumed to be known a priori. It is proposed to estimate and remove the deterministic terms such as mean,...

Testing the cointegrating rank of a vector autoregressive process with an intercept is considered. In addition to the likelihood ratio (LR) tests developed by Johansen and Juselius and others we also consider an alternative class of tests which is based on estimating the trend parameters of the...

The literature on systems cointegration tests is reviewed and the various sets of assumptions for the asymptotic validity of the tests are compared within a general unifying framework. The comparison includes likelihood ratio tests, Lagrange multiplier and Wald type tests, lag augmentation...

Unit root tests for time series with level shifts are considered. The level shift is assumed to occur at a known time point. In contrast to some other proposals the level shift is modeled as part of the intercept term of the stationary component of the data generation process which is separated...

Unit root tests are considered for time series which have a level shift at a known point in time. The shift can have a very general nonlinear form and additional deterministic mean and trend terms are allowed for. Prior to the tests the deterministic parts and other nuisance parameters of the...

It is argued that standard impulse response analysis based on vector autoregressive models has a number of shortcomings. Although the impulse responses are estimated quantities, measures for sampling variability such as confidence intervals are often not provided. If confidence intervals are...

An introduction to vector autoregressive (VAR) analysis is given with special emphasis on cointegration. The models, estimating their parameters and specifying the autoregressive order, the cointegrating rank and other restrictions are discussed. Possibilities for model validation are also...

Unit root tests for time series with level shifts of general form are considered when the timing of the shift is unknown. It is proposed to estimate the nuisance parameters of the data generation process including the shift date in a first step and apply standard unit root tests to the...