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

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  • Densing, M.

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.

Suggested Citation

  • Densing, M., 2012. "Occupation times of the Ornstein–Uhlenbeck process: Functional PCA and evidence from electricity prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5818-5826.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:5818-5826
    DOI: 10.1016/j.physa.2012.07.040
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    References listed on IDEAS

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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. 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.
    3. 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 361-375, March.
    4. 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.
    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.
    2. Davari-Ardakani, Hamed & Aminnayeri, Majid & Seifi, Abbas, 2014. "A study on modeling the dynamics of statistically dependent returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 35-51.

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