LEAST SQUARES AND IVX LIMIT THEORY IN SYSTEMS OF PREDICTIVE REGRESSIONS WITH GARCH INNOVATIONS
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含 GARCH 创新的预测回归系统：最小二乘与 IVX 极限理论
- 研究问题
- 当回归变量的持久性从近似平稳跨越到近单位根且创新具有 GARCH 异方差时，如何进行有效的最小二乘和 IVX 推断？
- 方法与思路
- 作者分析回归变量信号强度如何消除平稳 GARCH 对极限分布的影响，并调整 IVX–Wald 检验以涵盖纯平稳情形。
- 材料陈述的贡献
- 摘要称标准推断在所列信号增长条件下成立，调整后的 IVX–Wald 在规定的 GARCH 条件下覆盖近 I(0) 至近 I(1) 范围。
- 阅读关注点
- 应核对 κ_n 的增长约束、系统创新的协方差平稳条件、自标准化构造，以及纯平稳情况下 Wald 调整的具体形式。
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- 仅据所给 Crossref 摘要，不能将有效性推广到任意条件异方差或非平稳波动过程，也无法判断有限样本优势及版本变化。
原文摘要
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 $O_{p}\left ( n\kappa _{n}\right ) $ for arbitrary $\,\kappa _{n}\rightarrow \infty $ 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 $O_{p}\left ( n\right ) $ signal of stationary regressors but may be dominated by the $O_{p}\left ( n^{2}\right ) $ 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 $\kappa _{n}\rightarrow \infty $ and $\kappa _{n}/n\rightarrow 0$ 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 $\kappa _{n}\rightarrow \infty $ 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.