Non-parametric estimation of forecast distributions in non-Gaussian, non-linear state space models

Jason Ng, Catherine Forbes, Gael Martin and Brendan McCabe

International Journal of Forecasting, 2013, vol. 29, issue 3, 411-430

Abstract: The object of this paper is to produce non-parametric maximum likelihood estimates of forecast distributions in a general non-Gaussian, non-linear state space setting. The transition densities that define the evolution of the dynamic state process are represented in parametric form, but the conditional distribution of the non-Gaussian variable is estimated non-parametrically. The filtered and prediction distributions are estimated via a computationally efficient algorithm that exploits the functional relationship between the observed variable, the state variable and a measurement error with an invariant distribution. Simulation experiments are used to document the accuracy of the non-parametric method relative to both correctly and incorrectly specified parametric alternatives. In an empirical illustration, the method is used to produce sequential estimates of the forecast distribution of realized volatility on the S&P500 stock index during the recent financial crisis. A resampling technique for measuring sampling variation in the estimated forecast distributions is also demonstrated.

Keywords: Probabilistic forecasting; Non-Gaussian time series; Grid-based filtering; Penalized likelihood; Subsampling; Realized volatility (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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Related works:
Working Paper: Non-Parametric Estimation of Forecast Distributions in Non-Gaussian, Non-linear State Space Models (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:intfor:v:29:y:2013:i:3:p:411-430

DOI: 10.1016/j.ijforecast.2012.10.005

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