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DETERMINING THE COINTEGRATION RANK IN HETEROSKEDASTIC VAR MODELS OF UNKNOWN ORDER

Published online by Cambridge University Press:  20 September 2016

Giuseppe Cavaliere ,
Luca De Angelis ,
Anders Rahbek  and
A.M. Robert Taylor
Giuseppe Cavaliere
Affiliation:
University of Bologna
Luca De Angelis
Affiliation:
University of Bologna
Anders Rahbek
Affiliation:
University of Copenhagen
A.M. Robert Taylor*
Affiliation:
University of Essex
*
*Address correspondence to Robert Taylor, Essex Business School, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK; e-mail: rtaylor@essex.ac.uk.
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Abstract

We investigate the asymptotic and finite sample properties of a number of methods for estimating the cointegration rank in integrated vector autoregressive systems of unknown autoregressive order driven by heteroskedastic shocks. We allow for both conditional and unconditional heteroskedasticity of a very general form. We establish the conditions required on the penalty functions such that standard information criterion-based methods, such as the Bayesian information criterion [BIC], when employed either sequentially or jointly, can be used to consistently estimate both the cointegration rank and the autoregressive lag order. In doing so we also correct errors which appear in the proofs provided for the consistency of information-based estimators in the homoskedastic case by Aznar and Salvador (2002, Econometric Theory 18, 926–947). We also extend the corpus of available large sample theory for the conventional sequential approach of Johansen (1995, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press) and the associated wild bootstrap implementation thereof of Cavaliere, Rahbek, and Taylor (2014, Econometric Reviews 33, 606–650) to the case where the lag order is unknown. In particular, we show that these methods remain valid under heteroskedasticity and an unknown lag length provided the lag length is first chosen by a consistent method, again such as the BIC. The relative finite sample properties of the different methods discussed are investigated in a Monte Carlo simulation study. The two best performing methods in this study are a wild bootstrap implementation of the Johansen (1995, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press) procedure implemented with BIC selection of the lag length and joint IC approach (cf. Phillips, 1996, Econometrica 64, 763–812) which uses the BIC to jointly select the lag order and the cointegration rank.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 2 , April 2018 , pp. 349 - 382
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

We are grateful to the Editor, Peter Phillips, the Co-Editor, Michael Jansson, and two anonymous referees for their helpful comments on earlier versions of this paper. This work was supported by the Danish Council for Independent Research Sapere Aude | DFF Advanced Grant [grant number 12-124980], the Economic and Social Research Council [grant number ES/M01147X/1], and the Italian Ministry of Education, University and Research (MIUR), PRIN project “Multivariate statistical models for risk assessment.”

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