The Cointegrated VAR without Unit Roots: Representation Theory and Asymptotics

by   James A. Duffy, et al.

It has been known since Elliott (1998) that efficient methods of inference on cointegrating relationships break down when autoregressive roots are near but not exactly equal to unity. This paper addresses this problem within the framework of a VAR with non-unit roots. We develop a characterisation of cointegration, based on the impulse response function implied by the VAR, that remains meaningful even when roots are not exactly unity. Under this characterisation, the long-run equilibrium relationships between the series are identified with a subspace associated to the largest characteristic roots of the VAR. We analyse the asymptotics of maximum likelihood estimators of this subspace, thereby generalising Johansen's (1995) treatment of the cointegrated VAR with exactly unit roots. Inference is complicated by nuisance parameter problems similar to those encountered in the context of predictive regressions, and can be dealt with by approaches familiar from that setting.



There are no comments yet.


page 1

page 2

page 3

page 4


RANSAC Algorithms for Subspace Recovery and Subspace Clustering

We consider the RANSAC algorithm in the context of subspace recovery and...

Open problem: Tightness of maximum likelihood semidefinite relaxations

We have observed an interesting, yet unexplained, phenomenon: Semidefini...

On the one parameter unit-Lindley distribution and its associated regression model for proportion data

In this paper considering the transformation X=Y/1+Y, where Y ∼Lindley(θ...

Bayesian Subspace HMM for the Zerospeech 2020 Challenge

In this paper we describe our submission to the Zerospeech 2020 challeng...

Almost-Matching-Exactly for Treatment Effect Estimation under Network Interference

We propose a matching method that recovers direct treatment effects from...

Location of zeros for the partition function of the Ising model on bounded degree graphs

The seminal Lee-Yang theorem states that for any graph the zeros of the ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.