Predictive regression under various degrees of persistence and robust long-horizon regression

By Peter C. B. Phillips, Ji Hyung Lee. 2013

111 citations recorded by the source corpus.

The paper proposes a novel inference procedure for long-horizon predictive regression with persistent regressors, allowing the autoregressive roots to lie in a wide vicinity of unity. The invalidity of conventional tests when regressors are persistent has led to a large literature dealing with inference in predictive regressions with local to unity regressors. Magdalinos and Phillips (2009b) recently developed a new framework of extended IV procedures (IVX) that enables robust chi-square testing for a wider class of persistent regressors. We extend this robust procedure to an even wider parameter space in the vicinity of unity and apply the methods to long-horizon predictive regression. Existing methods in this model, which rely on simulated critical values by inverting tests under local to unity conditions, cannot be easily extended beyond the scalar regressor case or to wider autoregressive parametrizations. In contrast, the methods developed here lead to standard chi-square tests, allow for multivariate regressors, and include predictive processes whose roots may lie in a wide vicinity of unity. As such they have many potential applications in predictive regression. In addition to asymptotics under the null hypothesis of no predictability, the paper investigates validity under the alternative, showing how balance in the regression may be achieved through the use of localizing coefficients and developing local asymptotic power properties under such alternatives. These results help to explain some of the empirical difficulties that have been encountered in establishing predictability of stock returns.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/68582d9a2ec846a06a7c73669e613e68f56f32c2

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Citations in the corpus

Local Projection Inference Is Simpler and More Robust Than You Think (2020, background): “The behavior of plug-in AR impulse response estimates is also non-standard when ρ ≈ 1 and h ∝ T , see Phillips (1998), Pesavento and Rossi (2006, 2007), and Mikusheva (2012).”
Nonparametric Predictive Regression (2015, unknown): “j=0 φt+j ) ξ−t =: A ∗ n +B ∗ n, Following Wang et al. (2003) (see for example eq.”
On LASSO for predictive regression (2018, unknown): “In predictive regressions, Kostakis et al. (2014), Lee (2016) and Phillips and Lee (2013, 2016) provide inferential procedures in the presence of multiple predictors with various degrees of persistence.”