Co‐integration Rank Determination in Partial Systems Using Information Criteria

Abstract

We investigate the asymptotic and finite sample properties of the most widely used information criteria for co-integration rank determination in 'partial' systems, i.e. in co-integrated vector autoregressive (VAR) models where a sub-set of variables of interest is modelled conditional on another sub-set of variables. The asymptotic properties of the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn information criterion (HQC) are established, and consistency of BIC and HQC is proved. Notably, the consistency of BIC and HQC is robust to violations of weak exogeneity of the conditioning variables with respect to the co-integration parameters. More precisely, BIC and HQC recover the true co-integration rank from the partial system analysis also when the conditional model does not convey all information about the co-integration parameters. This result opens up interesting possibilities for practitioners who can now determine the co-integration rank in partial systems without being concerned about the weak exogeneity of the conditioning variables. A Monte Carlo experiment based on a large dimensional data generating process shows that BIC and HQC applied in partial systems perform reasonably well in small samples and comparatively better than 'traditional'methods for co-integration rank determination. We further show the usefulness of our approach and the benefits of the conditional system analysis in two empirical illustrations, both based on the estimation of VAR systems on US quarterly data. Overall, our analysis shows the gains of combining information criteria with partial system analysis.

Partial Cointegrated Vector Autoregressive Models with Structural Breaks in Deterministic Terms

“…Even so, the cointegrating relationships β X t−1 + γt form cross equation restrictions, so that maximum likelihood estimation involves a joint analysis of ( 3) and ( 6). The rank can be determined from a partial analysis using information criteria albeit without size control as argued by Cavaliere et al (2018).…”

“…Boswijk (1995) and Ericsson and MacKinnon (2002) explored the use of conditional autoregressive models. Recently, Cavaliere et al (2018) considered information criteria based on the HNJR test statistics. The second extension was a full cointegrated system with structural breaks in a constant level or linear trend, a model explored by Johansen et al (2000), referred to as JMN hereafter.…”

Timely and effective media coverage's role in the spread of Corona Virus Disease 2019

“…Since the Granger Causal Relation test is very susceptible to the lag of variables, it is usually used to test different lag lengths. 46 The Vector Autoregression (VAR) model is constructed for the variables. In 1980, Sims.…”

“…The smaller the values of the three parameters, the better the effect of the model under this lag. 46 In this paper, the test formula of 0–5 lag is respectively used for the test. In the Table 3 , the results are shown.…”

“…The idea of HQ is basically the same as that of AIC and SC, the difference lies in the penalties for newly added parameters that impair the prediction accuracy. The smaller the values of the three parameters, the better the effect of the model under this lag 46 . In this paper, the test formula of 0–5 lag is respectively used for the test.…”