On Confidence Intervals for Autoregressive Roots and Predictive Regression

By Peter C. B. Phillips. 2012

107 citations recorded by the source corpus.

Local to unity limit theory is used in applications to construct confidence intervals (CIs) for autoregressive roots through inversion of a unit root test (Stock (1991)). Such CIs are asymptotically valid when the true model has an autoregressive root that is local to unity (ρ = 1 + c/n), but are shown here to be invalid at the limits of the domain of definition of the localizing coefficient c because of a failure in tightness and the escape of probability mass. Failure at the boundary implies that these CIs have zero asymptotic coverage probability in the stationary case and vicinities of unity that are wider than O(n-super-−1/3). The inversion methods of Hansen (1999) and Mikusheva (2007) are asymptotically valid in such cases. Implications of these results for predictive regression tests are explored. When the predictive regressor is stationary, the popular Campbell and Yogo (2006) CIs for the regression coefficient have zero coverage probability asymptotically, and their predictive test statistic Q erroneously indicates predictability with probability approaching unity when the null of no predictability holds. These results have obvious cautionary implications for the use of the procedures in empirical practice.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/599c7c1060dcddd48a29b1be2ef01f382e96f8e3

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Citations in the corpus

NEARLY OPTIMAL TESTS WHEN A NUISANCE PARAMETER IS PRESENT UNDER THE NULL HYPOTHESIS (2015, methodology): “The persistence in x t is often modelled as a local-to-unity process (in the sense of Bobkoski (1983), Cavanagh (1985), Chan and Wei (1987) and Phillips (1987)) with r = r T = 1 − δ/T .”
Predictive quantile regression with persistent covariates: IVX-QR approach (2015, methodology): “The invalidity of the original CY-Q test for I(0)-MI regressors has been recently reported and a modi cation based on a uniformly valid CI (e.g., Mikusheva, 2007) was suggested in the literature (Phillips, 2014).”
Predictive regression under various degrees of persistence and robust long-horizon regression (2013, background): “Note that although the rate parameter α is generally unknown, it is also possible to consistently estimate this parameter in practice, as shown in Phillips (2012a).”
Nonparametric Predictive Regression (2015, unknown): “2(b) can be obtained using the same arguments as those above together with the limit theory of Wang et al. (2003). Phillips (2007) provides a strong approximation result in the shortmemory case under the stronger summability requirement  ∞ j=0 j φj < ∞.”