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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Chambers, Marcus J. 2016. The estimation of continuous time models with mixed frequency data. Journal of Econometrics, Vol. 193, Issue. 2, p. 390.

    Thornton, Michael A. and Chambers, Marcus J. 2016. The exact discretisation of CARMA models with applications in finance. Journal of Empirical Finance,

    Chambers, Marcus J. 2015. Testing for a Unit Root in a Near-Integrated Model with Skip-Sampled Data. Journal of Time Series Analysis, Vol. 36, Issue. 5, p. 630.

    Roebroeck, A. 2015. Brain Mapping.

    Kirshner, Hagai Unser, Michael and Ward, John Paul 2014. On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data. IEEE Transactions on Signal Processing, Vol. 62, Issue. 6, p. 1361.

    Thornton, Michael A. and Chambers, Marcus J. 2013. Continuous-time autoregressive moving average processes in discrete time: representation and embeddability. Journal of Time Series Analysis, Vol. 34, Issue. 5, p. 552.



  • Marcus J. Chambers (a1) and Michael A. Thornton (a2)
  • DOI:
  • Published online: 02 August 2011

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Corresponding author
*Address correspondence to Marcus J. Chambers, Department of Economics, University of Essex, Wivenhoe Park, Colchester, Essex CO4 3SQ, United Kingdom; e-mail:
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