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Fixed-B Asymptotics For The Studentized Mean From Time Series With Short, Long, Or Negative Memory

Author

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  • McElroy, Tucker
  • Politis, Dimitris N.

Abstract

This paper considers the problem of variance estimation for the 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 generalizes the short memory results of Kiefer and Vogelsang (2005, Econometric Theory 21, 1130–1164). In particular, our results highlight the dependence on the kernel (we include flat-top kernels), whether or not the kernel is nonzero at the boundary, and, most important, whether or not the process is short memory. Simulation studies support the importance of accounting for memory in the construction of confidence intervals for the mean.

Suggested Citation

  • 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(2), pages 471-481, April.
    • Handle: RePEc:cup:etheor:v:28:y:2012:i:02:p:471-481_00
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    Cited by:

    1. 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.
    2. 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.
    3. Wenger, Kai & Leschinski, Christian, 2021. "Fixed-bandwidth CUSUM tests under long memory," Econometrics and Statistics, Elsevier, vol. 20(C), pages 46-61.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Coroneo, Laura & Iacone, Fabrizio, 2025. "Testing for equal predictive accuracy with strong dependence," International Journal of Forecasting, Elsevier, vol. 41(3), pages 1073-1092.
    10. 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.
    11. 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.
    12. 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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