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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.

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  • 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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    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.
    3. Li Liu & Yumin Liu & Jong-Min Kim, 2019. "Sustainable Visual Analysis for Bank Non-Performing Loans and Government Debt Distress," Sustainability, MDPI, vol. 12(1), pages 1-21, December.

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