Limit Theory for Cointegrated Systems with Moderately Integrated and Moderately Explosive Regressors

• Main Authors: Magdalinos, Tassos, Peter C. B. PHILLIPS
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2009
• Subjects: Central limit theory; Cointegration; Di⁄usion; Explosive process; Invariance principle; Mixed normality; Moderate deviations; Unit root distribution; Weak dependence; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1808; https://ink.library.smu.edu.sg/context/soe_research/article/2807/viewcontent/Limit_theory_Moderately_Regressors_sv.pdf
• Institution: Singapore Management University

An asymptotic theory is developed for multivariate regression in cointegrated systems whose variables are moderately integrated or moderately explosive in the sense that they have autoregressive roots of the form rho(ni) = 1 + c(i)/n(alpha), involving moderate deviations from unity when alpha is an element of (0, 1) and c(i) is an element of R are constant parameters. When the data are moderately integrated in the stationary direction (with c(i) < 0), it is shown that least squares regression is consistent and asymptotically normal but suffers from significant bias, related to simultaneous equations bias. In the moderately explosive case (where c(i) > 0) the limit theory is mixed normal with Cauchy-type tail behavior, and the rate of convergence is explosive, as in the case of a moderately explosive scalar autoregression (Phillips and Magdalinos, 2007, Journal of Econometrics 136, 115-130). Moreover, the limit theory applies without any distributional assumptions and for weakly dependent errors under conventional moment conditions, so an invariance principle holds, unlike the well-known case of an explosive autoregression. This theory validates inference in cointegrating regression with mildly explosive regressors. The special case in which the regressors themselves have a common explosive component is also considered.