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Nonparametric density estimation for positive time series

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  • BOUEZMARNI, Taoufik
  • ROMBOUTS, Jeroen V. K.

Abstract

The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For i.i.d. data several solutions have been put forward to solve this boundary problem. In this paper we propose the gamma kernel estimator as density estimator for positive data from a stationary -mixing process. We derive the mean integrated squared error, almost sure convergence and asymptotic normality. In a Monte Carlo study, where we generate data from an autoregressive conditional duration model and a stochastic volatility model, we find that the gamma kernel outperforms the local linear density estimator. An application to data from financial transaction durations, realized volatility and electricity price data is provided.

Suggested Citation

  • BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V. K., 2006. "Nonparametric density estimation for positive time series," CORE Discussion Papers 2006085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2006085
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    Cited by:

    1. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    2. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V. K., 2006. "Density and hazard rate estimation for censored and a-mixing data using gamma kernels," CORE Discussion Papers 2006118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.
    4. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K., 2007. "Nonparametric density estimation for multivariate bounded data," CORE Discussion Papers 2007065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Bouezmarni, T. & Rombouts, J.V.K., 2009. "Semiparametric multivariate density estimation for positive data using copulas," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2040-2054, April.
    6. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.

    More about this item

    Keywords

    gamma kernel; nonparametric density estimation; mixing process; transaction durations; realised volatility;

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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