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Distribution Theory for the Studentized Mean for Long, Short, and Negative Memory Time Series

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  • McElroy, Tucker S.
  • 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. Extensive 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.

Suggested Citation

  • McElroy, Tucker S. & Politis, Dimitris N., 2012. "Distribution Theory for the Studentized Mean for Long, Short, and Negative Memory Time Series," University of California at San Diego, Economics Working Paper Series qt35c7r55c, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt35c7r55c
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    4. 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.
    5. repec:eee:ecolet:v:156:y:2017:i:c:p:145-150 is not listed on IDEAS

    More about this item

    Keywords

    Social and Behavioral Sciences; Kernel; Lag-windows; Overdifferencing; Spectral estimation; Subsampling; Tapers; Unit-root problem;

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