Testing cointegration in infinite order vector autoregressive processes
type: Item
instance of: scholarly article
title: Testing cointegration in infinite order vector autoregressive processes
zbMATH Open document ID: 0922.62119
DOI: 10.1016/S0304-4076(97)00036-5
author: Pentti Saikkonen
author: Ritva Luukkonen
published in: Journal of Econometrics
publication date: 1999-10-17T00:00:00Z
review text: Tests are investigated to find the cointegration rank in infinite order \(n\)-dimensional autoregressive processes: \[ y_{1t}= Ay_{2t}+ u_{1t}, \quad\Delta y_{2t}= u_{2t}, \] where \(\dim y_{1t} =n_1\), \(\dim y_{2t}= n_2\) \((n_1+n_2+n)\), and residuals have an infinite order autoregressive representation. On tests the null hypothesis \(H(n_1)\): ``cointegrating rank equal to \(n_1\)'' against the alternative hypothesis \(\overline H(n_1)\): ``cointegrating rank larger than \(n_1\)''. It is shown that the original versions of the likelihood ratio tests for finite order Gaussian VAR processes [see, e.g., \textit{S. Johanson}, Econometrica 59, No. 6, 1551-1580 (1991; Zbl 0755.62087)] can be extended to infinite order non-Gaussian processes. Moreover, new tests are suggested for the cases where intercept terms are included in the cointegration relations \(z_t=m+y_r\). The intercept terms are estimated using generalised least squares. The resulting test statistics have under the null hypothesis the same limiting distributions as in the case where the model contains no intercept term or when the values of the intercept term are a priori known. The new tests have good power properties compared with their previous counterparts. These properties are confirmed by a simulation study.
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 1083050
zbMATH Keywords: infinite other vector autoregression
zbMATH Keywords: cointegration
zbMATH Keywords: likelihood ratio tests
zbMATH Keywords: generalised least squares
reviewed by: Tomáš Cipra
MaRDI profile type: Publication
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full work available at URL: s0304-4076(97)00036-5
OpenAlex ID: W2053863891
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description: scientific article; zbMATH DE number 1083050