IDEAS home Printed from https://ideas.repec.org/p/cep/stiecm/520.html
   My bibliography  Save this paper

On Discrete Sampling Of Time-Varyingcontinuous-Time Systems

Author

Listed:
  • Peter Robinson

Abstract

We consider a multivariate continuous time process, generated by a system of linear stochastic differential equations, driven by white noise and involving coefficients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points (though equal spacing significantly simplifies matters). Such settings represent partial extensions of ones studied extensively by A.R. Bergstrom. A model for the observed time series is deduced. Initially we focus on a first-order model, but higher-order ones are discussed in case of equally-spaced observations. Some discussion of issues of statistical inference is included.

Suggested Citation

  • Peter Robinson, 2007. "On Discrete Sampling Of Time-Varyingcontinuous-Time Systems," STICERD - Econometrics Paper Series 520, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:520
    as

    Download full text from publisher

    File URL: https://sticerd.lse.ac.uk/dps/em/em520.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robinson, Peter M., 1977. "The construction and estimation of continuous time models and discrete approximations in econometrics," Journal of Econometrics, Elsevier, vol. 6(2), pages 173-197, September.
    2. Michel De Vroey & Pierre Malgrange, 2016. "Macroeconomics," Chapters, in: Gilbert Faccarello & Heinz D. Kurz (ed.), Handbook on the History of Economic Analysis Volume III, chapter 27, pages 372-390, Edward Elgar Publishing.
    3. Robinson, P. M., 1977. "Estimation of a time series model from unequally spaced data," Stochastic Processes and their Applications, Elsevier, vol. 6(1), pages 9-24, November.
    4. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-823, September.
    5. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    6. Bergstrom,Albert Rex & Nowman,Khalid Ben, 2012. "A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends," Cambridge Books, Cambridge University Press, number 9781107411234, October.
    7. Guy Mélard & Annie Herteleer‐de Schutter, 1989. "Contributions To Evolutionary Spectral Theory," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(1), pages 41-63, January.
    8. Hallin, Marc, 1978. "Mixed autoregressive-moving average multivariate processes with time-dependent coefficients," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 567-572, December.
    9. Peter C. B. Phillips & Jun Yu, 2005. "Comments on “A selective overview of nonparametric methods in financial econometricsâ€Â," Finance Working Papers 22469, East Asian Bureau of Economic Research.
    10. Bergstrom, A. R., 1988. "The History of Continuous-Time Econometric Models," Econometric Theory, Cambridge University Press, vol. 4(3), pages 365-383, December.
    11. Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
    12. Guy Melard & Annie Herteleer, 1989. "Contributions to the evolutionary spectral theory," ULB Institutional Repository 2013/13708, ULB -- Universite Libre de Bruxelles.
    13. Peter C.B.Phillips & Jun Yu, "undated". "Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance," Working Papers CoFie-08-2009, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    14. Dunsmuir, W., 1983. "A central limit theorem for estimation in Gaussian stationary time series observed at unequally spaced times," Stochastic Processes and their Applications, Elsevier, vol. 14(3), pages 279-295, March.
    15. Peter C. B. Phillips & Jun Yu, 2005. "Comments on “A Selective Overview of Nonparametric Methods in Financial Econometrics” by Jianqing Fan," Working Papers 08-2005, Singapore Management University, School of Economics.
    16. Robinson, P M, 1976. "The Estimation of Linear Differential Equations with Constant Coefficients," Econometrica, Econometric Society, vol. 44(4), pages 751-764, July.
    17. Bergstrom, Albert Rex, 1983. "Gaussian Estimation of Structural Parameters in Higher Order Continuous Time Dynamic Models," Econometrica, Econometric Society, vol. 51(1), pages 117-152, January.
    Full references (including those not matched with items on IDEAS)

    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. Robinson, Peter, 2007. "On discrete sampling of time-varying continuous-time systems," LSE Research Online Documents on Economics 6795, London School of Economics and Political Science, LSE Library.
    2. Jun Yu, 2009. "Econometric Analysis of Continuous Time Models : A Survey of Peter Phillips’ Work and Some New Results," Microeconomics Working Papers 23046, East Asian Bureau of Economic Research.
    3. Yu, Jun, 2014. "Econometric Analysis Of Continuous Time Models: A Survey Of Peter Phillips’S Work And Some New Results," Econometric Theory, Cambridge University Press, vol. 30(4), pages 737-774, August.
    4. Peter C.B.Phillips & Jun Yu, "undated". "Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance," Working Papers CoFie-08-2009, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    5. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.
    6. Wang, Xiaohu & Phillips, Peter C.B. & Yu, Jun, 2011. "Bias in estimating multivariate and univariate diffusions," Journal of Econometrics, Elsevier, vol. 161(2), pages 228-245, April.
    7. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    8. Fryzlewicz, Piotr & Nason, Guy P., 2006. "Haar-Fisz estimation of evolutionary wavelet spectra," LSE Research Online Documents on Economics 25227, London School of Economics and Political Science, LSE Library.
    9. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    10. Thornton, Michael A. & Chambers, Marcus J., 2017. "Continuous time ARMA processes: Discrete time representation and likelihood evaluation," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 48-65.
    11. A. R. Bergstrom, 2001. "Stability and wage acceleration in macroeconomic models of cyclical growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 327-340.
    12. Péter Kevei, 2018. "Asymptotic moving average representation of high-frequency sampled multivariate CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 467-487, April.
    13. Fryzlewicz, Piotr & Nason, Guy P., 2004. "Smoothing the wavelet periodogram using the Haar-Fisz transform," LSE Research Online Documents on Economics 25231, London School of Economics and Political Science, LSE Library.
    14. Koo, Bonsoo & Linton, Oliver, 2012. "Estimation of semiparametric locally stationary diffusion models," Journal of Econometrics, Elsevier, vol. 170(1), pages 210-233.
    15. Nowman, K. Ben, 2011. "Gaussian estimation of continuous time diffusions of UK interest rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1618-1624.
    16. Massimiliano Marcellino & Oscar Jorda, "undated". "Stochastic Processes Subject to Time-Scale Transformations: An Application to High-Frequency FX Data," Working Papers 164, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Peter C. B. Phillips & Jun Yu, 2009. "Simulation-Based Estimation of Contingent-Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3669-3705, September.
    18. Andreou, Elena & Ghysels, Eric & Kourtellos, Andros, 2010. "Regression models with mixed sampling frequencies," Journal of Econometrics, Elsevier, vol. 158(2), pages 246-261, October.
    19. repec:cep:stiecm:/2013/568 is not listed on IDEAS
    20. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    21. Piotr Borkowski & Jan Mielniczuk, 2010. "Postmodel selection estimators of variance function for nonlinear autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 50-63, January.

    More about this item

    Keywords

    Stochastic differential equations; time-varying coefficients; discrete sampling; irregular sampling.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    Statistics

    Access and download statistics

    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:cep:stiecm:520. 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: the person in charge (email available below). General contact details of provider: https://sticerd.lse.ac.uk/_new/publications/ .

    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.