Least squares and IVX limit theory in systems of predictive regressions with GARCH innovations
Least squares and IVX limit theory in systems of predictive regressions with GARCH innovations
The paper examines the effect of conditional heteroskedasticity on least squares inference in stochastic regression models of unknown integration order and proposes an inference procedure that is robust to models within the (near) I(0)-(near) I(1) range with GARCH innovations. We show that a regressor signal of exact order Op (mκn) for arbitrary κn → ∞ is sufficient to eliminate stationary GARCH effects from the limit distributions of least squares based estimators and self-normalized test statistics. The above order dominates the Op (n) signal of stationary regressors but may be dominated by the Op (n2) signal of I(1) regressors, thereby showing that least squares invariance to GARCH effects is not an exclusively I(1) phenomenon but extends to processes with persistence degree arbitrarily close to stationarity. The theory validates standard inference for self normalized test statistics based on the ordinary least squares estimator when κn → ∞ and κn/n → 0 and the IVX estimator (Phillips and Magdalinos (2009a), Econometric Inference in the Vicinity of Unity. Working paper, Singapore Management University; Kostakis, Magdalinos, and Stamatogiannis, 2015a, Review of Financial Studies 28(5), 1506-1553.) when κn → ∞ and the innovation sequence of the system is a covariance stationary vec-GARCH process. An adjusted version of the IVX-Wald test is shown to also accommodate GARCH effects in purely stationary regressors, thereby extending the procedure's validity over the entire (near) I(0)-(near) I(1) range of regressors under conditional heteroskedasticity in the innovations. It is hoped that the wide range of applicability of this adjusted IVX-Wald test, established in Theorem 4.4, presents an advantage for the procedure's suitability as a tool for applied research.
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
Magdalinos, Tassos
(2021)
Least squares and IVX limit theory in systems of predictive regressions with GARCH innovations.
Econometric Theory.
(doi:10.1017/S0266466621000086).
Abstract
The paper examines the effect of conditional heteroskedasticity on least squares inference in stochastic regression models of unknown integration order and proposes an inference procedure that is robust to models within the (near) I(0)-(near) I(1) range with GARCH innovations. We show that a regressor signal of exact order Op (mκn) for arbitrary κn → ∞ is sufficient to eliminate stationary GARCH effects from the limit distributions of least squares based estimators and self-normalized test statistics. The above order dominates the Op (n) signal of stationary regressors but may be dominated by the Op (n2) signal of I(1) regressors, thereby showing that least squares invariance to GARCH effects is not an exclusively I(1) phenomenon but extends to processes with persistence degree arbitrarily close to stationarity. The theory validates standard inference for self normalized test statistics based on the ordinary least squares estimator when κn → ∞ and κn/n → 0 and the IVX estimator (Phillips and Magdalinos (2009a), Econometric Inference in the Vicinity of Unity. Working paper, Singapore Management University; Kostakis, Magdalinos, and Stamatogiannis, 2015a, Review of Financial Studies 28(5), 1506-1553.) when κn → ∞ and the innovation sequence of the system is a covariance stationary vec-GARCH process. An adjusted version of the IVX-Wald test is shown to also accommodate GARCH effects in purely stationary regressors, thereby extending the procedure's validity over the entire (near) I(0)-(near) I(1) range of regressors under conditional heteroskedasticity in the innovations. It is hoped that the wide range of applicability of this adjusted IVX-Wald test, established in Theorem 4.4, presents an advantage for the procedure's suitability as a tool for applied research.
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Accepted/In Press date: 19 January 2021
e-pub ahead of print date: 23 March 2021
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© The Author(s), 2021.
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Local EPrints ID: 448179
URI: http://eprints.soton.ac.uk/id/eprint/448179
ISSN: 0266-4666
PURE UUID: 85364986-9675-4590-988b-aa8d9b184142
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Date deposited: 14 Apr 2021 16:31
Last modified: 16 Mar 2024 11:57
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