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Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting

Author

Listed:
  • Fuqi Chen

    (University of Western Ontario)

  • Rogemar Mamon

    (University of Western Ontario
    University of the Philippines Visayas)

  • Sévérien Nkurunziza

    (University of Windsor)

Abstract

Determining accurately when regime and structural changes occur in various time-series data is critical in many social and natural sciences. We develop and show further the equivalence of two consistent estimation techniques in locating the change point under the framework of a generalised version of the one-dimensional Ornstein–Uhlenbeck process. Our methods are based on the least sum of squared error and the maximum log-likelihood approaches. The case where both the existence and the location of the change point are unknown is investigated and an informational methodology is employed to address these issues. Numerical illustrations are presented to assess the methods’ performance.

Suggested Citation

  • Fuqi Chen & Rogemar Mamon & Sévérien Nkurunziza, 2018. "Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 807-853, August.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:4:d:10.1007_s10463-017-0610-4
    DOI: 10.1007/s10463-017-0610-4
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    1. Date, Paresh & Mamon, Rogemar & Tenyakov, Anton, 2013. "Filtering and forecasting commodity futures prices under an HMM framework," Energy Economics, Elsevier, vol. 40(C), pages 1001-1013.
    2. Sangyeol Lee & Meihui Guo, 2015. "Monitoring change point for diffusion parameter based on discretely observed sample from stochastic differential equation models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(5), pages 609-625, September.
    3. Iacus, Stefano M. & Yoshida, Nakahiro, 2012. "Estimation for the change point of volatility in a stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1068-1092.
    4. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    5. Erlwein, Christina & Benth, Fred Espen & Mamon, Rogemar, 2010. "HMM filtering and parameter estimation of an electricity spot price model," Energy Economics, Elsevier, vol. 32(5), pages 1034-1043, September.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    8. Liang, Zhibin & Yuen, Kam Chuen & Guo, Junyi, 2011. "Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 207-215, September.
    9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    10. Herold Dehling & Brice Franke & Thomas Kott & Reg Kulperger, 2014. "Change point testing for the drift parameters of a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 1-18, April.
    11. Herold Dehling & Brice Franke & Thomas Kott, 2010. "Drift estimation for a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 175-192, October.
    12. Robbins, Michael W. & Lund, Robert B. & Gallagher, Colin M. & Lu, QiQi, 2011. "Changepoints in the North Atlantic Tropical Cyclone Record," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 89-99.
    13. Robert J. Elliott & Craig A. Wilson, 2007. "The Term Structure of Interest Rates in a Hidden Markov Setting," International Series in Operations Research & Management Science, in: Rogemar S. Mamon & Robert J. Elliott (ed.), Hidden Markov Models in Finance, chapter 2, pages 15-30, Springer.
    14. Ashish Sen & S. Srivastava, 1975. "On tests for detecting change in mean when variance is unknown," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 479-486, December.
    15. Peter Guttorp & Stephan R. Sain & Christopher K. Wikle & Colin Gallagher & Robert Lund & Michael Robbins, 2012. "Changepoint detection in daily precipitation data," Environmetrics, John Wiley & Sons, Ltd., vol. 23(5), pages 407-419, August.
    16. Elias, R.S. & Wahab, M.I.M. & Fang, L., 2014. "A comparison of regime-switching temperature modeling approaches for applications in weather derivatives," European Journal of Operational Research, Elsevier, vol. 232(3), pages 549-560.
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