Publication Type

Journal Article

Version

publishedVersion

Publication Date

12-2019

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 -> infinity 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 -> infinity, all three statistics, including the HAR test, diverge and fail to control size as n -> infinity. These findings are relevant to high-dimensional nonstationary time series regressions where machine learning methods may be employed.

Keywords

HAR inference, Karhunen-Loeve representation, spurious regression, t-statistics

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometrics

Volume

7

Issue

4

First Page

1

Last Page

28

ISSN

2225-1146

Identifier

10.3390/econometrics7040050

Publisher

MDPI

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.3390/econometrics7040050

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