Har testing for spurious regression in trend

Artikel

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

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Econometrics ; ISSN: 2225-1146 ; Volume: 7 ; Year: 2019 ; Issue: 4 ; Pages: 1-28 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft ; Hypothesis Testing: General ; Semiparametric and Nonparametric Methods: General ; Single Equation Models; Single Variables: Panel Data Models; Spatio-temporal Models
• Subject: t-statistics ; HAR inference ; Karhunen– ; Loève representation ; spurious regression

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Phillips, Peter C. B. ; Wang, XiaoHu ; Zhang, Yonghui
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2019

Further information

• DOI: doi:10.3390/econometrics7040050
• Handle: http://hdl.handle.net/10419/247550
• Last update: 10.03.2025, 11:44 AM CET