Impulse response functions (IRFs) are crucial for analyzing the dynamic interactions of macroeconomic variables in vector autoregressive (VAR) models. However, traditional IRF estimation methods often have limitations with assumptions on variable ordering and restrictive identification...

In this paper the theory on the estimation of vector autoregressive (VAR) models for I(2) processes is extended to the case of long VAR approximation of more general processes. Hereby the order of the autoregression is allowed to tend to infinity at a certain rate depending on the sample size....

Likelihood ratio tests of over-identifying restrictions on the common trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained)...

A state space model with an unobserved multivariate random walk and a linear observation equation is studied. The purpose is to find out when the extracted trend cointegrates with its estimator, in the sense that a linear combination is asymptotically stationary. It is found that this result...

This paper discusses the notion of cointegrating space for linear processes integrated of any order. It first shows that the notions of (polynomial) cointegrating vectors and of root functions coincide. Second, it discusses how the cointegrating space can be defined (i) as a vector space of...

A multivariate, non-Bayesian, regression-based, or feasible generalized least squares (GLS)-based approach is proposed to estimate time-varying VAR parameter models. Although it has been known that the Kalman-smoothed estimate can be alternatively estimated using GLS for univariate models, we...

This article was prepared for the Special Issue "Celebrated Econometricians: Katarina Juselius and Søren Johansen" of Econometrics. It is based on material recorded on 30 October 2018 in Copenhagen. It explores Søren Johansen’s research, and discusses inter alia the following issues:...

We propose a method to explore the causal transmission of an intervention through two endogenous variables of interest. We refer to the intervention as a catalyst variable. The method is based on the reduced-form system formed from the conditional distribution of the two endogenous variables...

When using vector autoregressive (VAR) models for approximating time series, a key step is the selection of the lag length. Often this is performed using information criteria, even if a theoretical justification is lacking in some cases. For stationary processes, the asymptotic properties of the...

A causal vector autoregressive (CVAR) model is introduced for weakly stationary multivariate processes, combining a recursive directed graphical model for the contemporaneous components and a vector autoregressive model longitudinally. Block Cholesky decomposition with varying block sizes is...