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Faculty of Economics

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Harvey, A. C. and Oryshchenko, V.

Kernel density estimation for time series data

International Journal of Forecasting

Vol. 28(1) pp. 3-14 (2012)

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.

Keywords: Exponential smoothing, Probability integral transform, Time-varying quantiles, Signal extraction, Stock returns

Author links: Andrew Harvey  

Publisher's Link: https://doi.org/10.1016/j.ijforecast.2011.02.016



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