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Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter

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  • Ahn, Kwang Woo
  • Chan, Kung-Sik

Abstract

The problem of estimating a nonlinear state-space model whose state process is driven by an ordinary differential equation (ODE) or a stochastic differential equation (SDE), with discrete-time data is studied. A new estimation method is proposed based on minimizing the conditional least squares (CLS) with the conditional mean function computed approximately via the unscented Kalman filter (UKF). Conditions are derived for the UKF–CLS estimator to preserve the limiting properties of the exact CLS estimator, namely, consistency and asymptotic normality, under the framework of infill asymptotics, i.e. sampling is increasingly dense over a fixed domain. The efficacy of the proposed method is demonstrated by simulation and a real application.

Suggested Citation

  • Ahn, Kwang Woo & Chan, Kung-Sik, 2014. "Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 243-254.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:243-254
    DOI: 10.1016/j.csda.2013.07.038
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    References listed on IDEAS

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    1. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non‐Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    3. Frits Bijleveld & Jacques Commandeur & Siem Jan Koopman & Kees van Montfort, 2010. "Multivariate non‐linear time series modelling of exposure and risk in road safety research," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 145-161, January.
    4. Liang, Hua & Wu, Hulin, 2008. "Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1570-1583.
    5. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    6. Kwang Ahn & Kung-Sik Chan, 2013. "On the convergence rate of the unscented transformation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 889-912, October.
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    Cited by:

    1. Camba-Méndez, Gonzalo & Serwa, Dobromił, 2016. "Market perception of sovereign credit risk in the euro area during the financial crisis," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 168-189.

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