A bootstrap stationarity test for predictive regression invalidity

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors un...

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Main Authors: Georgiev, Iliyan, Harvey, David I., Leybourne, Stephen J., Taylor, A.M. Robert
Format: Article
Language:English
Published: Taylor & Francis 2017
Subjects:
Online Access:https://eprints.nottingham.ac.uk/45335/
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author Georgiev, Iliyan
Harvey, David I.
Leybourne, Stephen J.
Taylor, A.M. Robert
author_facet Georgiev, Iliyan
Harvey, David I.
Leybourne, Stephen J.
Taylor, A.M. Robert
author_sort Georgiev, Iliyan
building Nottingham Research Data Repository
collection Online Access
description In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid with the result that both the finite sample and asymptotic size of the predictability tests can be significantly infated, with the potential therefore to spuriously indicate predictability. In response we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroskedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test. This entails demonstrating that the asymptotic distribution of the bootstrap statistic, conditional on the data, is the same (to first-order) as the asymptotic null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have important applications beyond the present context. An illustration is given by re-examining the results relating to U.S. stock returns data in Campbell and Yogo (2006).
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spelling nottingham-453352018-10-02T04:30:12Z https://eprints.nottingham.ac.uk/45335/ A bootstrap stationarity test for predictive regression invalidity Georgiev, Iliyan Harvey, David I. Leybourne, Stephen J. Taylor, A.M. Robert In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid with the result that both the finite sample and asymptotic size of the predictability tests can be significantly infated, with the potential therefore to spuriously indicate predictability. In response we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroskedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test. This entails demonstrating that the asymptotic distribution of the bootstrap statistic, conditional on the data, is the same (to first-order) as the asymptotic null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have important applications beyond the present context. An illustration is given by re-examining the results relating to U.S. stock returns data in Campbell and Yogo (2006). Taylor & Francis 2017-10-02 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/45335/1/predreg.pdf Georgiev, Iliyan, Harvey, David I., Leybourne, Stephen J. and Taylor, A.M. Robert (2017) A bootstrap stationarity test for predictive regression invalidity. Journal of Business and Economic Statistics . ISSN 1537-2707 Predictive regression; Granger causality; persistence; stationarity test; fixed regressor wild bootstrap; conditional distribution http://www.tandfonline.com/doi/abs/10.1080/07350015.2017.1385467 doi:10.1080/07350015.2017.1385467 doi:10.1080/07350015.2017.1385467
spellingShingle Predictive regression; Granger causality; persistence; stationarity test; fixed regressor wild bootstrap; conditional distribution
Georgiev, Iliyan
Harvey, David I.
Leybourne, Stephen J.
Taylor, A.M. Robert
A bootstrap stationarity test for predictive regression invalidity
title A bootstrap stationarity test for predictive regression invalidity
title_full A bootstrap stationarity test for predictive regression invalidity
title_fullStr A bootstrap stationarity test for predictive regression invalidity
title_full_unstemmed A bootstrap stationarity test for predictive regression invalidity
title_short A bootstrap stationarity test for predictive regression invalidity
title_sort bootstrap stationarity test for predictive regression invalidity
topic Predictive regression; Granger causality; persistence; stationarity test; fixed regressor wild bootstrap; conditional distribution
url https://eprints.nottingham.ac.uk/45335/
https://eprints.nottingham.ac.uk/45335/
https://eprints.nottingham.ac.uk/45335/