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On Discrete Sampling Of Time-Varyingcontinuous-Time Systems

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  • 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
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    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.
    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.
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    Full references (including those not matched with items on IDEAS)

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    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

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