Further Results on Size and Power of Heteroskedasticity and Autocorrelation Robust Tests, with an Application to Trend Testing

Pötscher, Benedikt M. and Preinerstorfer, David (2017): Further Results on Size and Power of Heteroskedasticity and Autocorrelation Robust Tests, with an Application to Trend Testing.

Abstract

We complement the theory developed in Preinerstorfer and Pötscher (2016) with further finite sample results on size and power of heteroskedasticity and autocorrelation robust tests. These allow us, in particular, to show that the sufficient conditions for the existence of size-controlling critical values recently obtained in Pötscher and Preinerstorfer (2016) are often also necessary. We furthermore apply the results obtained to tests for hypotheses on deterministic trends in stationary time series regressions, and find that many tests currently used are strongly size-distorted.

• Item Type: MPRA Paper
• Language: English
• Keywords: size-distortion, autocorrelation and heteroskedasticity robust testing, trend testing
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59 817-858.

Andrews, D. W. K. and Monahan, J. C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, 60 953-966.

Bunzel, H. and Vogelsang, T. J. (2005). Powerful trend function tests that are robust to strong serial correlation, with an application to the Prebisch-Singer hypothesis. Journal of Business & Economic Statistics, 23 381-394.

Davies, R. B. (1980). Algorithm AS 155: The distribution of a linear combination of chi2 random variables. Journal of the Royal Statistical Society. Series C, 29 323-333.

Eicker, F. (1967). Limit theorems for regressions with unequal and dependent errors. In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66). Univ. California Press, Berkeley, Calif., Vol. I: Statistics, pp. 59-82.

Grenander, U. (1954). On the estimation of regression coefficients in the case of an autocorrelated disturbance. The Annals of Mathematical Statistics, 25 252{272.

Harvey, D. I., Leybourne, S. J. and Taylor, A. R. (2007). A simple, robust and powerful test of the trend hypothesis. Journal of Econometrics, 141 1302-1330.

Kiefer, N. M. and Vogelsang, T. J. (2002a). Heteroskedasticity-autocorrelation robust standard errors using the Bartlett kernel without truncation. Econometrica, 70 2093-2095.

Kiefer, N. M. and Vogelsang, T. J. (2002b). Heteroskedasticity-autocorrelation robust testing using bandwidth equal to sample size. Econometric Theory, 18 1350-1366.

Kiefer, N. M. and Vogelsang, T. J. (2005). A new asymptotic theory for heteroskedasticityautocorrelation robust tests. Econometric Theory, 21 1130-1164.

Kiefer, N. M., Vogelsang, T. J. and Bunzel, H. (2000). Simple robust testing of regression hypotheses. Econometrica, 68 695-714.

Long, J. S. and Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. The American Statistician, 54 217-224.

Newey, W. K. and West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55 703-708.

Newey, W. K. and West, K. D. (1994). Automatic lag selection in covariance matrix estimation. The Review of Economic Studies, 61 631-653.

Perron, P. and Yabu, T. (2009). Estimating deterministic trends with an integrated or stationary noise component. Journal of Econometrics, 151 56-69.

Pötscher, B. M. and Preinerstorfer, D. (2016). Controlling the size of autocorrelation robust tests. arXiv:1612.06127.

Preinerstorfer, D. (2016). acrt: Autocorrelation robust testing. Version 1.0. URL https://CRAN.R-project.org/package=acrt.

Preinerstorfer, D. (2017). Finite sample properties of tests based on prewhitened nonparametric covariance estimators. Electron. J. Statist., 11 2097-2167.

Preinerstorfer, D. and Pötscher, B. M. (2016). On size and power of heteroskedasticity and autocorrelation robust tests. Econometric Theory, 32 261-358.

Robinson, G. (1979). Conditional properties of statistical procedures. Annals of Statistics, 7 742-755.

Vogelsang, T. J. (1998). Trend function hypothesis testing in the presence of serial correlation. Econometrica, 66 123-148.