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The History of Continuous-Time Econometric Models

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  • Bergstrom, A. R.

Abstract

Although it is only during the last decade that continuous-time models have been extensively used in applied econometric work, the development of statistical methods applicable to such models commenced over 40 years ago. The first significant contribution to the problem of estimating the parameters of continuous-time stochastic models from discrete data was made by the British statistician Bartlett [1946] only three years after the pioneering contribution of Haavelmo [1943] on simultaneous equations models. Moreover, by this time the fundamental mathematical theory of continuous-time stochastic models was already well developed, major contributions having been made by some of the leading mathematicians of the twentieth century, including Einstein, Weiner, and Kolmogorov.

Suggested Citation

  • Bergstrom, A. R., 1988. "The History of Continuous-Time Econometric Models," Econometric Theory, Cambridge University Press, vol. 4(3), pages 365-383, December.
  • Handle: RePEc:cup:etheor:v:4:y:1988:i:03:p:365-383_01
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    Cited by:

    1. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    2. 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.
    3. Nomikos, Nikos K. & Soldatos, Orestes A., 2010. "Modelling short and long-term risks in power markets: Empirical evidence from Nord Pool," Energy Policy, Elsevier, vol. 38(10), pages 5671-5683, October.
    4. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    5. J. Oud, 2010. "Second-order stochastic differential equation model as an alternative for the ALT and CALT models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(2), pages 203-215, June.
    6. Peter Fuleky, 2012. "On the choice of the unit period in time series models," Applied Economics Letters, Taylor & Francis Journals, vol. 19(12), pages 1179-1182, August.
    7. Tianshun Yan & Yanyong Zhao & Wentao Wang, 2020. "Likelihood-based estimation of a semiparametric time-dependent jump diffusion model of the short-term interest rate," Computational Statistics, Springer, vol. 35(2), pages 539-557, June.
    8. Tucker McElroy, 2013. "Forecasting continuous-time processes with applications to signal extraction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 439-456, June.
    9. Sy‐Miin Chow & Guangjian Zhang, 2008. "Continuous‐time modelling of irregularly spaced panel data using a cubic spline model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(1), pages 131-154, February.
    10. 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.
    11. Hermann Singer, 2011. "Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(4), pages 375-413, December.
    12. Arie ten Cate, 2004. "Refinement of the partial adjustment model using continuous-time econometrics," CPB Discussion Paper 41, CPB Netherlands Bureau for Economic Policy Analysis.
    13. 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.
    14. Tucker S. McElroy & Thomas M. Trimbur, 2007. "Continuous time extraction of a nonstationary signal with illustrations in continuous low-pass and band-pass filtering," Finance and Economics Discussion Series 2007-68, Board of Governors of the Federal Reserve System (U.S.).
    15. Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011. "Modelling Electricity Prices: International Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
    16. 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.
    17. Marc J. M. H. Delsing & Johan H. L. Oud, 2008. "Analyzing reciprocal relationships by means of the continuous‐time autoregressive latent trajectory model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(1), pages 58-82, February.
    18. 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.

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