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A Note on the Behaviour of Nonparametric Density and Spectral Density Estimators at Zero Points of their Support

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  • Efstathios Paparoditis
  • Dimitris N. Politis

Abstract

type="main" xml:id="jtsa12142-abs-0001"> The asymptotic behaviour of nonparametric estimators of the stationary density and of the spectral density function of a stationary process have been studied in some detail in the last 50–60years. Nevertheless, less is known about the behaviour of these estimators when the target function happens to vanish at the point of interest. In the article at hand, we fill this gap and show that asymptotic normality still holds true but with super-efficient and different rates of convergence for the density and for the spectral density estimators that are affected also by the dependence structure of the process.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:37:y:2016:i:2:p:182-194
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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(2), pages 471-481, April.
    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. Harald E. Krogstad, 1982. "On The Covariance Of The Periodogram," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 195-207, May.
    4. Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1218-1245, August.
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