IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v70y2018i4d10.1007_s10463-017-0610-4.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-017-0610-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-017-0610-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    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. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    6. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sévérien Nkurunziza, 2023. "Estimation and Testing in Multivariate Generalized Ornstein-Uhlenbeck Processes with Change-Points," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 351-400, February.
    2. Yunhong Lyu & Sévérien Nkurunziza, 2023. "Inference in generalized exponential O–U processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 581-618, October.
    3. Sévérien Nkurunziza & Lei Shen, 2020. "Inference in a multivariate generalized mean-reverting process with a change-point," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 199-226, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sévérien Nkurunziza & Lei Shen, 2020. "Inference in a multivariate generalized mean-reverting process with a change-point," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 199-226, April.
    2. Sévérien Nkurunziza & Pei Patrick Zhang, 2018. "Estimation and testing in generalized mean-reverting processes with change-point," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 191-215, April.
    3. Michael W. Robbins & Colin M. Gallagher & Robert B. Lund, 2016. "A General Regression Changepoint Test for Time Series Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 670-683, April.
    4. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    5. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    6. Heng Xiong & Rogemar Mamon, 2018. "Putting a price tag on temperature," Computational Management Science, Springer, vol. 15(2), pages 259-296, June.
    7. Joanna Janczura, 2014. "Pricing electricity derivatives within a Markov regime-switching model: a risk premium approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 1-30, February.
    8. Chang Guo & Xiaoyang Zhuo & Corina Constantinescu & Olivier Menoukeu Pamen, 2018. "Optimal Reinsurance-Investment Strategy Under Risks of Interest Rate, Exchange Rate and Inflation," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1477-1502, December.
    9. Robert J. Elliott & Tak Kuen Siu, 2016. "Pricing regime-switching risk in an HJM interest rate environment," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1791-1800, December.
    10. Bu Ruijun & Cheng Jie & Hadri Kaddour, 2017. "Specification analysis in regime-switching continuous-time diffusion models for market volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(1), pages 65-80, February.
    11. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    12. Sévérien Nkurunziza, 2023. "Estimation and Testing in Multivariate Generalized Ornstein-Uhlenbeck Processes with Change-Points," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 351-400, February.
    13. Stefano M. Iacus & Nakahiro Yoshida, 2010. "Numerical Analysis of Volatility Change Point Estimators for Discretely Sampled Stochastic Differential Equations," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 39(1‐2), pages 107-127, February.
    14. Chuong Luong & Nikolai Dokuchaev, 2016. "Modeling Dependency Of Volatility On Sampling Frequency Via Delay Equations," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-21, June.
    15. Ben S. Bernanke & Vincent R. Reinhart & Brian P. Sack, 2004. "Monetary Policy Alternatives at the Zero Bound: An Empirical Assessment," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 35(2), pages 1-100.
    16. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    17. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    18. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    19. Gonçalo Jacinto & Patrícia A. Filipe & Carlos A. Braumann, 2022. "Profit Optimization of Cattle Growth with Variable Prices," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1917-1952, September.
    20. Olivier Le Courtois, 2022. "On the Diversification of Fixed Income Assets," Risks, MDPI, vol. 10(2), pages 1-21, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:70:y:2018:i:4:d:10.1007_s10463-017-0610-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.