The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Continuous and Discrete Time Models

  • Christopher A. Sims
Reference work entry


Most modelling of economic time series works with discrete time, yet time is in fact continuous. While in many instances simple intuitive connections exist between results with discrete time data and the underlying continuous time dynamics, it is possible for discretization to create bias or have unintuitive effects. Some economics literature investigates such distortions. It is also possible to estimate explicitly continuous-time models, using discrete data. This approach raises its own difficulties, but has become more usable as computing power and the techniques to exploit it have improved.


Approximation theory Continuous and discrete time models Distributed lags Dynamic stochastic general equilibrium models Granger causal priority Markov chain Monte Carlo methods Martingales No-arbitrage models Stochastic differential equations Vector autoregressions Wiener process 

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  1. Aїt-Sahalia, Y. 2007. Estimating continuous-time models using discretely sampled data. In Advances in economics and econometrics, theory and applications. Ninth World Congress, ed. R. Blundell, T. Persson, and W.K. Newey, vol. 3. Cambridge: Cambridge University Press.Google Scholar
  2. Bergstrom, A.R., ed. 1976. Statistical inference in continuous time economic models. Amsterdam: North-Holland.Google Scholar
  3. Bergstrom, A.R. 1983. Gaussian estimation of structural parameters in higher order continuous time dynamic models. Econometrica 51: 117–152.CrossRefGoogle Scholar
  4. Geweke, J. 1978. Temporal aggregation in the multiple regression model. Econometrica 46: 643–662.CrossRefGoogle Scholar
  5. Hansen, L.P., and T.J. Sargent, eds. 1991. Rational expectations econometrics. Boulder and Oxford: Westview Press.Google Scholar
  6. Harrison, J.M., R. Pitbladdo, and S.M. Schaefer. 1984. Continuous price processes in frictionless markets have infinite variation. Journal of Business 57: 353–365.CrossRefGoogle Scholar
  7. Johannes, M., and N. Polson. 2006. MCMC methods for continuous-time financial econometrics. In Handbook of financial econometrics, ed. Y. Aït-Sahalia and L.P. Hansen. Amsterdam: North-Holland.Google Scholar
  8. Marcet, A. 1991. Temporal aggregation of economic time series. In Rational expectations econometrics, ed. L.P. Hansen and T.J. Sargent. Boulder and Oxford: Westview Press.Google Scholar
  9. Rozanov, Yu.A. 1967. Stationary random processes, trans A. Feinstein. San Francisco/Cambridge/London/Amsterdam: Holden-Day.Google Scholar
  10. Sims, C.A. 1971. Approximate specifications in distributed lag models. In Proceedings of the 38th Session, Bulletin of the International Statistical Institute 44, Book 1.Google Scholar
  11. Sims, C.A., and S. Maheswaran. 1993. Empirical implications of arbitrage-free asset markets. In Models, methods and applications of econometrics, ed. P.C.B. Phillips. Oxford: Blackwell.Google Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Christopher A. Sims
    • 1
  1. 1.