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Determining the cointegration rank in heteroskedastic VAR models of unknown order

Cavaliere, Giuseppe and De Angelis, Luca and Rahbek, Anders and Taylor, AM Robert (2018) 'Determining the cointegration rank in heteroskedastic VAR models of unknown order.' Econometric Theory, 34 (02). 349 - 382. ISSN 0266-4666

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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.

Item Type: Article
Additional Information: license: Copyright © Cambridge University Press 2016
Subjects: H Social Sciences > HG Finance
Divisions: Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Essex Finance Centre
Depositing User: Jim Jamieson
Date Deposited: 24 Aug 2016 12:41
Last Modified: 20 Jul 2018 16:15
URI: http://repository.essex.ac.uk/id/eprint/17455

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