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Fixed-b asymptotics for the studentized mean from time series with short, long or negative memory

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  • Politis, D N
  • McElroy, Tucker S

Abstract

This paper considers the problem of distribution estimation for the studentized sample mean in the context of Long Memory and Negative Memory time series dynamics, adopting the fixed-bandwidth approach now popular in the econometrics literature. The distribution theory complements the Short Memory results of Kiefer and Vogelsang (2005). In particular, our results highlight the dependence on the employed kernel, whether or not the taper is nonzero at the boundary, and most importantly whether or not the process has short memory. We also demonstrate that small-bandwidth approaches fail when long memory or negative memory is present since the limiting distribution is either a point mass at zero or degenerate. Extensive numerical work provides approximations to the quantiles of the asymptotic distribution for a range of tapers and memory parameters; these quantiles can be used in practice for the construction of confidence intervals and hypothesis tests for the mean of the time series.

Suggested Citation

  • Politis, D N & McElroy, Tucker S, 2009. "Fixed-b asymptotics for the studentized mean from time series with short, long or negative memory," University of California at San Diego, Economics Working Paper Series qt70c4x0sq, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt70c4x0sq
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    1. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
    2. Politis, Dimitris, 2005. "Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices," University of California at San Diego, Economics Working Paper Series qt7qg2m9rz, Department of Economics, UC San Diego.
    3. Hurvich, Clifford M., 2002. "Multistep forecasting of long memory series using fractional exponential models," International Journal of Forecasting, Elsevier, vol. 18(2), pages 167-179.
    4. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
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    1. Politis, Dimitris, 2012. "On The Behavior Of Nonparametric Density And Spectral Density Estimators At Zero Points Of Their Support," University of California at San Diego, Economics Working Paper Series qt40g0z0tz, Department of Economics, UC San Diego.
    2. McElroy, Tucker S. & Politis, Dimitris N., 2014. "Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics," Journal of Econometrics, Elsevier, vol. 182(1), pages 211-225.
    3. Kruse, Robinson & Leschinski, Christian & Will, Michael, 2016. "Comparing Predictive Accuracy under Long Memory - With an Application to Volatility Forecasting," Hannover Economic Papers (HEP) dp-571, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    4. Fabrizio Iacone & Stephen J. Leybourne & A. M. Robert Taylor, 2014. "A FIXED- b TEST FOR A BREAK IN LEVEL AT AN UNKNOWN TIME UNDER FRACTIONAL INTEGRATION," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 40-54, January.
    5. McElroy, Tucker & Politis, Dimitris N., 2013. "Distribution theory for the studentized mean for long, short, and negative memory time series," Journal of Econometrics, Elsevier, vol. 177(1), pages 60-74.
    6. Hualde, Javier & Iacone, Fabrizio, 2017. "Fixed bandwidth asymptotics for the studentized mean of fractionally integrated processes," Economics Letters, Elsevier, vol. 150(C), pages 39-43.
    7. Javier Hualde & Fabrizio Iacone, 2015. "Autocorrelation robust inference using the Daniell kernel with fixed bandwidth," Discussion Papers 15/14, Department of Economics, University of York.
    8. Wenger, Kai & Leschinski, Christian, 2021. "Fixed-bandwidth CUSUM tests under long memory," Econometrics and Statistics, Elsevier, vol. 20(C), pages 46-61.
    9. Kai Wenger & Christian Leschinski & Philipp Sibbertsen, 2019. "Change-in-mean tests in long-memory time series: a review of recent developments," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 237-256, June.
    10. Efstathios Paparoditis & Dimitris N. Politis, 2016. "A Note on the Behaviour of Nonparametric Density and Spectral Density Estimators at Zero Points of their Support," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 182-194, March.
    11. Hualde, Javier & Iacone, Fabrizio, 2017. "Revisiting inflation in the euro area allowing for long memory," Economics Letters, Elsevier, vol. 156(C), pages 145-150.

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