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Kernel density estimation for time series data

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  • Harvey, Andrew
  • Oryshchenko, Vitaliy

Abstract

A time-varying probability density function, or the corresponding cumulative distribution function, may be estimated nonparametrically by using a kernel and weighting the observations using schemes derived from time series modelling. The parameters, including the bandwidth, may be estimated by maximum likelihood or cross-validation. Diagnostic checks may be carried out directly on residuals given by the predictive cumulative distribution function. Since tracking the distribution is only viable if it changes relatively slowly, the technique may need to be combined with a filter for scale and/or location. The methods are applied to data on the NASDAQ index and the Hong Kong and Korean stock market indices.

Suggested Citation

  • Harvey, Andrew & Oryshchenko, Vitaliy, 2012. "Kernel density estimation for time series data," International Journal of Forecasting, Elsevier, vol. 28(1), pages 3-14.
    • Handle: RePEc:eee:intfor:v:28:y:2012:i:1:p:3-14
    DOI: 10.1016/j.ijforecast.2011.02.016
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    References listed on IDEAS

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    9. Gourieroux, C. & Jasiak, J., 2008. "Dynamic quantile models," Journal of Econometrics, Elsevier, vol. 147(1), pages 198-205, November.
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    Cited by:

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    2. Marcin Dec, 2021. "From point through density valuation to individual risk assessment in the discounted cash flows method," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5621-5635, October.
    3. Ayoub Ammy-Driss & Matthieu Garcin, 2020. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Papers 2007.10727, arXiv.org, revised Nov 2021.
    4. Fourier, Jean-Baptiste Joseph, 2022. "Indicador Bernardos: un nuevo indicador clave en el análisis del mercado de las criptomonedas y de la conducta humana ante lo desconocido," OSF Preprints 87brk, Center for Open Science.
    5. Wang, Jianzhou & Hu, Jianming & Ma, Kailiang, 2016. "Wind speed probability distribution estimation and wind energy assessment," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 881-899.
    6. Harvey, A., 2021. "Score-driven time series models," Cambridge Working Papers in Economics 2133, Faculty of Economics, University of Cambridge.
    7. Liu, Wei & Semeyutin, Artur & Lau, Chi Keung Marco & Gozgor, Giray, 2020. "Forecasting Value-at-Risk of Cryptocurrencies with RiskMetrics type models," Research in International Business and Finance, Elsevier, vol. 54(C).
    8. Marcin Dec, 2019. "From point through density valuation to individual risk assessment in the discounted cash flows method," GRAPE Working Papers 35, GRAPE Group for Research in Applied Economics.
    9. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Papers 2305.13123, arXiv.org.
    10. Yan, Hanhuan & Han, Liyan, 2019. "Empirical distributions of stock returns: Mixed normal or kernel density?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 473-486.
    11. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723.
    12. Gu, Wentao & Peng, Yiqing, 2019. "Forecasting the market return direction based on a time-varying probability density model," Technological Forecasting and Social Change, Elsevier, vol. 148(C).
    13. Matthieu Garcin & Jules Klein & Sana Laaribi, 2020. "Estimation of time-varying kernel densities and chronology of the impact of COVID-19 on financial markets," Papers 2007.09043, arXiv.org, revised Mar 2022.
    14. Matthieu Garcin & Jules Klein & Sana Laaribi, 2022. "Estimation of time-varying kernel densities and chronology of the impact of COVID-19 on financial markets," Working Papers hal-02901988, HAL.
    15. Ammy-Driss, Ayoub & Garcin, Matthieu, 2023. "Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    16. Bram van Os, 2023. "Information-Theoretic Time-Varying Density Modeling," Tinbergen Institute Discussion Papers 23-037/III, Tinbergen Institute.
    17. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Working Papers hal-04102815, HAL.
    18. Arora Siddharth & Little Max A. & McSharry Patrick E., 2013. "Nonlinear and nonparametric modeling approaches for probabilistic forecasting of the US gross national product," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(4), pages 395-420, September.
    19. Semeyutin, Artur & O’Neill, Robert, 2019. "A brief survey on the choice of parameters for: “Kernel density estimation for time series data”," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).

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