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Occupation times of the Ornstein–Uhlenbeck process: Functional PCA and evidence from electricity prices

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  • Densing, M.
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    Abstract

    We discuss the functional principal component analysis (FPCA) of the occupation times of the Ornstein–Uhlenbeck process. For the eigenvalue problem of the covariance operator of the occupation times we derive the corresponding integral equation in the large time limit and we solve numerically for the principal components. The formulation applies the path-integral approach of Feynman and Kac. The principal components are compared with those from empirical electricity price processes on energy markets. The results indicate that FPCA of the occupation times is a suitable tool in stochastic energy modeling to generate moderately-sized scenario trees.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112007091
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 391 (2012)
    Issue (Month): 23 ()
    Pages: 5818-5826

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    Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:5818-5826

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Ornstein–Uhlenbeck process; Occupation time; Functional principal component analysis; Electricity price; PCA;

    References

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Bessembinder, Hendrik, et al, 1995. " Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure," Journal of Finance, American Finance Association, vol. 50(1), pages 361-75, March.
    3. Jorion, Philippe & Sweeney, Richard J., 1996. "Mean reversion in real exchange rates: evidence and implications for forecasting," Journal of International Money and Finance, Elsevier, vol. 15(4), pages 535-550, August.
    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    5. Bertram, William K., 2005. "A threshold model for Australian Stock Exchange equities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 561-576.
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    Cited by:
    1. Densing, M., 2013. "Dispatch planning using newsvendor dual problems and occupation times: Application to hydropower," European Journal of Operational Research, Elsevier, vol. 228(2), pages 321-330.

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