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...

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...

Starting from a linear error correction model the stability and linearity of a German M1 moneyt demand function are investigated, applying smooth transition regression techniques. Using seasonally unadjusted data from 1961 (1) to 1990 (2) it is found that the money demand equation is both linear...

Impulse response functions from time series models are standard tools for analyzing the relationship between economic variables. The asymptotic distribution of orthogonalized impulse responses is derived under the assumption that finite order vector autoregressive (VAR) models are fitted to time...

It is investigated whether euro area variables can be forecast better based on synthetic time series for the pre-euro period or by using just data from Germany for the pre-euro period. Our forecast comparison is based on quarterly data for the period 1970Q1-2003Q4 for 10 macroeconomic variables....

Tests for Granger-causality have been performed in numerous empirical studies. These tests are usually based on finite order vector autoregressive (VAR) processes, and the assumption is made that the model fitted to the available data corresponds to the true data generating mechanism. In the...

In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. These bands may be based on frequentist or Bayesian methods. If they are based on the joint distribution in the Bayesian framework or the joint asymptotic...

In vector autoregressive analysis confidence intervals for individual impulse responses are typically reported to indicate the sampling uncertainty in the estimation results. A range of methods are reviewed and a new proposal is made for constructing joint confidence bands, given a prespecified...