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Robust trend inference with series variance estimator and testing-optimal smoothing parameter

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  • Sun, Yixiao

Abstract

The paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model. The trends are estimated by the OLS estimator and the long run variance (LRV) matrix is estimated by a series type estimator with carefully selected basis functions. Regardless of whether the number of basis functions K is fixed or grows with the sample size, the Wald statistic converges to a standard distribution. It is shown that critical values from the fixed-K asymptotics are second-order correct under the large-K asymptotics. A new practical approach is proposed to select K that addresses the central concern of hypothesis testing: the selected smoothing parameter is testing-optimal in that it minimizes the type II error while controlling for the type I error. Simulations indicate that the new test is as accurate in size as the nonstandard test of Vogelsang and Franses (2005) and as powerful as the corresponding Wald test based on the large-K asymptotics. The new test therefore combines the advantages of the nonstandard test and the standard Wald test while avoiding their main disadvantages (power loss and size distortion, respectively).

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 164 (2011)
Issue (Month): 2 (October)
Pages: 345-366

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Handle: RePEc:eee:econom:v:164:y:2011:i:2:p:345-366

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Asymptotic expansion F-distribution Hotelling's T2 distribution Long run variance Robust standard error Series method Testing-optimal smoothing parameter choice Trend inference Type I and type II errors;

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References

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  1. Vogelsang, Timothy J. & Franses, Philip Hans, 2001. "Testing for Common Deterministic Trend Slopes," Working Papers 01-15, Cornell University, Center for Analytic Economics.
  2. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  3. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, 01.
  4. Hashimzade, Nigar & Vogelsang, Timothy, 2006. "Fixed-b Asymptotic Approximation of the Sampling Behavior of Nonparametric Spectral Density Estimators," Working Papers 06-04, Cornell University, Center for Analytic Economics.
  5. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation for Research in Economics, Yale University.
  6. Phillips, Peter C.B. & Sun, Yixiao & Jin, Sainan, 2004. "Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation," University of California at San Diego, Economics Working Paper Series qt6mf9q2rt, Department of Economics, UC San Diego.
  7. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1331-1352, December.
  8. Kiefer, Nicholas M., 2001. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using the Bartlett Kernel without Truncation," Working Papers 01-13, Cornell University, Center for Analytic Economics.
  9. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
  10. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests," Working Papers 05-08, Cornell University, Center for Analytic Economics.
  11. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  12. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1350-1366, December.
  13. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix: Some properties and applications," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153207, Tilburg University.
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Citations

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Cited by:
  1. Sun, Yixiao, 2013. "Fixed-smoothing Asymptotics in a Two-step GMM Framework," University of California at San Diego, Economics Working Paper Series qt64x4z265, Department of Economics, UC San Diego.
  2. Chen, Xiaohong & Liao, Zhipeng & Sun, Yixiao, 2014. "Sieve inference on possibly misspecified semi-nonparametric time series models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 639-658.
  3. Zhang, Xianyang & Shao, Xiaofeng, 2013. "On a general class of long run variance estimators," Economics Letters, Elsevier, vol. 120(3), pages 437-441.
  4. Sun, Yixiao, 2013. "Let's Fix It: Fixed-b Asymptotics versus Small-b Asymptotics in Heteroscedasticity and Autocorrelation Robust Inference," University of California at San Diego, Economics Working Paper Series qt8x8307rz, Department of Economics, UC San Diego.
  5. Peter C.B. Phillips & Zhipeng Liao, 2012. "Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications," Cowles Foundation Discussion Papers 1871, Cowles Foundation for Research in Economics, Yale University.
  6. Sun, Yixiao, 2014. "Fixed-smoothing Asymptotics and Asymptotic F and t Tests in the Presence of Strong Autocorrelation," University of California at San Diego, Economics Working Paper Series qt8479f4s2, Department of Economics, UC San Diego.
  7. Yonghui Zhang & Liangjun Su & Peter C. B. Phillips, 2012. "Testing for common trends in semi‐parametric panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 56-100, 02.
  8. Sun, Yixiao & Kim, Min Seong, 2012. "Simple and powerful GMM over-identification tests with accurate size," Journal of Econometrics, Elsevier, vol. 166(2), pages 267-281.
  9. Xiaohong Chen & Zhipeng Liao & Yixiao Sun, 2012. "Sieve Inference on Semi-nonparametric Time Series Models," Cowles Foundation Discussion Papers 1849, Cowles Foundation for Research in Economics, Yale University.
  10. Min Seong Kim & Yixiao Sun, 2012. "Asymptotic F Test in a GMM Framework with Cross Sectional Dependence," Working Papers 032, Ryerson University, Department of Economics.

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