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A higher order correlation unscented Kalman filter

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  • Oliver Grothe

Abstract

Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential estimation of diffusion parameters, e.g., volatility, which are not correlated with the observations is not possible. While other filters overcome this problem with simulations, we extend the measurement update of the Gaussian two-moment filters by a higher order correlation measurement update. We explicitly state formulas for a higher order unscented Kalman filter within a continuous-discrete state space. We demonstrate the filter in the context of parameter estimation of an Ornstein-Uhlenbeck process.

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  • Oliver Grothe, 2012. "A higher order correlation unscented Kalman filter," Papers 1207.4300, arXiv.org.
    • Handle: RePEc:arx:papers:1207.4300
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    3. Crowder, Martin, 1986. "On Consistency and Inconsistency of Estimating Equations," Econometric Theory, Cambridge University Press, vol. 2(3), pages 305-330, December.
    4. Heyde, C. C., 1987. "On combining quasi-likelihood estimating functions," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 281-287.
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