LIMIT THEORY FOR COINTEGRATED SYSTEMS WITH MODERATELY INTEGRATED AND MODERATELY EXPLOSIVE REGRESSORS

By Tassos Magdalinos, Peter C. B. Phillips. Econometric Theory, 2009

91 citations recorded by the source corpus.

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 ρni = 1 + ci/nα, involving moderate deviations from unity when α ∈ (0, 1) and ci ∈ ℝ are constant parameters. When the data are moderately integrated in the stationary direction (with ci < 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 ci > 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.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3f74c33c701a2c56e4af19afb449f02306d7ce9c

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Citations in the corpus

Predictive regression under various degrees of persistence and robust long-horizon regression (2013, background): “2 Asymptotic analysis of the invalidity in this construction and confirmatory finite sample simulations are given in Phillips (2012b). Lee (2012, Section 4) also reports simulation results confirming the problem in predictive regression settings.”
Robust econometric inference for stock return predictability (2011, unknown): “…processes, with ci in (3) being large in absolute value (Phillips 1987), or, more formally, as belonging to the class P(iii) of near-stationary processes established by Phillips and Magdalinos (2007) and extended to multivariate systems of regression equations by Magdalinos and Phillips (2009).”
Mildly explosive autoregression under weak and strong dependence (2012, background): “Multivariate extensions are included in Magdalinos and Phillips (2008).”
Instrumental variable and variable addition based inference in predictive regressions (2015, background): “If αT = 1 − a/T η, xt is mildly (or moderately) integrated in the sense of Phillips and Magdalinos (2007) and Magdalinos and Phillips (2009).”
UNIT ROOT AND COINTEGRATING LIMIT THEORY WHEN INITIALIZATION IS IN THE INFINITE PAST (2008, unknown): “A similar situation occurs in explosively cointegrated systems with repeated roots, i.e., systems with a (possibly mildly) explosive coefficient matrix that does not have distinct latent roots (see Phillips and Magdalinos, 2008, and Magdalinos and Phillips, 2009, for details).”
Econometric Inference in the Vicinity of Unity. 1 (2009, methodology): “Present econometric methodology of inference in cointegrating regression is extended to mildly integrated time series of the type introduced by Magdalinos and Phillips (2007, 2009) .”