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Distribution theory for the studentized mean for long, short, and negative memory time series

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  • McElroy, Tucker
  • Politis, Dimitris N.

Abstract

We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the first-difference of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically. We also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size, extending known results to the case of flat-top tapers. We adopt the fixed proportion bandwidth perspective in our empirical section, presenting two methods for estimating the limiting critical values—both the subsampling method and a plug-in approach. Simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean. Both methods perform well–although the subsampling method appears to be better sized–and provide a viable framework for conducting inference for the mean. In summary, we supply a unified asymptotic theory that covers all different types of memory under a single umbrella.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 177 (2013)
Issue (Month): 1 ()
Pages: 60-74

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Handle: RePEc:eee:econom:v:177:y:2013:i:1:p:60-74

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

Related research

Keywords: Kernel; Lag-windows; Overdifferencing; Spectral estimation; Subsampling; Tapers; Unit-root problem;

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  1. McElroy, Tucker & Politis, Dimitris N., 2012. "Fixed-B Asymptotics For The Studentized Mean From Time Series With Short, Long, Or Negative Memory," Econometric Theory, Cambridge University Press, vol. 28(02), pages 471-481, April.
  2. 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.
  3. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
  4. Agnieszka Jach & Tucker McElroy & Dimitris N. Politis, 2012. "Subsampling inference for the mean of heavy‐tailed long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 96-111, 01.
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  9. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2009. "Two estimators of the long-run variance: Beyond short memory," Journal of Econometrics, Elsevier, vol. 150(1), pages 56-70, May.
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  16. Robinson, P.M., 2005. "Robust Covariance Matrix Estimation: Hac Estimates With Long Memory/Antipersistence Correction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 171-180, February.
  17. Sun, Yixiao, 2003. "A Convergent t-statistic in Spurious Regressions," University of California at San Diego, Economics Working Paper Series qt150457tv, Department of Economics, UC San Diego.
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