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Varying kernel marginal density estimator for a positive time series

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  • N. Balakrishna
  • Hira L. Koul

Abstract

This paper analyses the large sample behaviour of a varying kernel density estimator of the marginal density of a non-negative stationary and ergodic time series that is also strongly mixing. In particular we obtain an approximation for bias, mean square error and establish asymptotic normality of this density estimator. We also derive an almost sure uniform consistency rate over bounded intervals of this estimator. A finite sample simulation shows some superiority of the proposed density estimator over the one based on a symmetric kernel.

Suggested Citation

  • N. Balakrishna & Hira L. Koul, 2017. "Varying kernel marginal density estimator for a positive time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 531-552, July.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:531-552
    DOI: 10.1080/10485252.2017.1324968
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    References listed on IDEAS

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    1. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    2. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
    3. Manganelli, Simone, 2005. "Duration, volume and volatility impact of trades," Journal of Financial Markets, Elsevier, vol. 8(4), pages 377-399, November.
    4. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    5. Wolfgang Härdle & Helmut Lütkepohl & Rong Chen, 1997. "A Review of Nonparametric Time Series Analysis," International Statistical Review, International Statistical Institute, vol. 65(1), pages 49-72, April.
    6. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    7. Olivier SCAILLET, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Guassian Kernels," LIDAM Discussion Papers IRES 2001017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    8. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    9. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    10. Gao, Jiti & Kim, Nam Hyun & Saart, Patrick W., 2015. "A misspecification test for multiplicative error models of non-negative time series processes," Journal of Econometrics, Elsevier, vol. 189(2), pages 346-359.
    11. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," LIDAM Discussion Papers CORE 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Hira L. Koul & Weixing Song, 2013. "Large sample results for varying kernel regression estimates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 829-853, December.
    13. Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
    14. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    15. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-582, June.
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