The University of Southampton
University of Southampton Institutional Repository

HAR testing for spurious regression with trend

HAR testing for spurious regression with trend
HAR testing for spurious regression with trend
The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given the potential for spurious relationships in trend formulations. Following a longstanding tradition in the spurious regression literature, this paper investigates the asymptotic and finite sample properties of these test statistics in several spurious regression contexts, including regression of stochastic trends on time polynomials and regressions among independent random walks. Concordant with existing theory (Phillips, 1986, 1998; Sun, 2004, 2014b), the usual t test and HAC standardized test fail to control size as the sample size n !1 in these spurious formulations, whereas HAR tests converge to well-defined limit distributions in each case and therefore have the capacity to be consistent and control size. However, it is shown that when the number of trend regressors K !1; all three statistics, including the HAR test, diverge and fail to control size as n !1. These findings are relevant to high dimensional nonstationary time series regressions where machine learning methods may be employed.
2225-1146
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Xiaohu
907f95ee-4a76-4803-9ac1-4336e057a016
Zhang, Yonghui
68eb75e5-3aab-4ce8-9c46-c30c53e68fd8
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Xiaohu
907f95ee-4a76-4803-9ac1-4336e057a016
Zhang, Yonghui
68eb75e5-3aab-4ce8-9c46-c30c53e68fd8

Phillips, Peter Charles Bonest, Wang, Xiaohu and Zhang, Yonghui (2019) HAR testing for spurious regression with trend. Econometrics. (In Press)

Record type: Article

Abstract

The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given the potential for spurious relationships in trend formulations. Following a longstanding tradition in the spurious regression literature, this paper investigates the asymptotic and finite sample properties of these test statistics in several spurious regression contexts, including regression of stochastic trends on time polynomials and regressions among independent random walks. Concordant with existing theory (Phillips, 1986, 1998; Sun, 2004, 2014b), the usual t test and HAC standardized test fail to control size as the sample size n !1 in these spurious formulations, whereas HAR tests converge to well-defined limit distributions in each case and therefore have the capacity to be consistent and control size. However, it is shown that when the number of trend regressors K !1; all three statistics, including the HAR test, diverge and fail to control size as n !1. These findings are relevant to high dimensional nonstationary time series regressions where machine learning methods may be employed.

Text
three-tests-Rev_1 - Accepted Manuscript
Restricted to Repository staff only until 30 January 2020.
Request a copy

More information

Accepted/In Press date: 30 September 2019

Identifiers

Local EPrints ID: 435265
URI: https://eprints.soton.ac.uk/id/eprint/435265
ISSN: 2225-1146
PURE UUID: e741f971-ab61-4fd1-b083-956d39222e4b
ORCID for Peter Charles Bonest Phillips: ORCID iD orcid.org/0000-0003-2341-0451

Catalogue record

Date deposited: 29 Oct 2019 17:30
Last modified: 29 Nov 2019 01:33

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×