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The Estimation of Open Higher-Order Continuous Time Dynamic Models with Mixed Stock and Flow Data

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  • Bergstrom, A. R.

Abstract

This article extends recent work on the Gaussian or quasi-maximum likelihood estimation of the parameters of a closed higher-order continuous time dynamic model by introducing exogenous variables into the model The method presented yields exact maximum likelihood estimates when the innovations are Gaussian and the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under more general conditions. It is applicable, in principle, to a system of any order with mixed stock and iow data. The precise formulas for its implementation are derived, in this article, for a second-order system in which both the endog-enous and exogenous variables are a mixture of stock and flow variables.

Suggested Citation

  • Bergstrom, A. R., 1986. "The Estimation of Open Higher-Order Continuous Time Dynamic Models with Mixed Stock and Flow Data," Econometric Theory, Cambridge University Press, vol. 2(03), pages 350-373, December.
  • Handle: RePEc:cup:etheor:v:2:y:1986:i:03:p:350-373_01
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    Cited by:

    1. Theodore Simos, 2008. "The exact discrete model of a system of linear stochastic differential equations driven by fractional noise," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1019-1031, November.
    2. Chambers, Marcus J, 1992. "Estimation of a Continuous-Time Dynamic Demand System," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(1), pages 53-64, Jan.-Marc.
    3. 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.
    4. Chambers, Marcus J., 1999. "Discrete time representation of stationary and non-stationary continuous time systems," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 619-639, February.
    5. Wymer Clifford R., 2012. "Continuous-Tme Econometrics of Structural Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-28, April.
    6. repec:eee:finana:v:52:y:2017:i:c:p:119-129 is not listed on IDEAS
    7. Peter Aling & Shakill Hassan, 2012. "No-Arbitrage One-Factor Models Of The South African Term Structure Of Interest Rates," South African Journal of Economics, Economic Society of South Africa, vol. 80(3), pages 301-318, September.
    8. J. Roderick McCrorie, 2000. "The Likelihood of a Continuous-time Vector Autoregressive Model," Working Papers 419, Queen Mary University of London, School of Economics and Finance.
    9. repec:eee:dyncon:v:79:y:2017:i:c:p:48-65 is not listed on IDEAS
    10. 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.
    11. Oguz Asirim, 1996. "Alternative Theories of Consumption and an Application to the Turkish Economy," Discussion Papers 9604, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    12. Episcopos, Athanasios, 2000. "Further evidence on alternative continuous time models of the short-term interest rate," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 10(2), pages 199-212, June.
    13. Roderick McCrorie, J., 2001. "Interpolating exogenous variables in continuous time dynamic models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1399-1427, September.
    14. Byers, S. L. & Nowman, K. B., 1998. "Forecasting U.K. and U.S. interest rates using continuous time term structure models," International Review of Financial Analysis, Elsevier, vol. 7(3), pages 191-206.
    15. 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(04), pages 737-774, August.
    16. Nowman, K. Ben & Saltoglu, Burak, 2003. "Continuous time and nonparametric modelling of U.S. interest rate models," International Review of Financial Analysis, Elsevier, vol. 12(1), pages 25-34.
    17. Nowman, K. Ben, 2002. "The volatility of Japanese interest rates: evidence for Certificate of Deposit and Gensaki rates," International Review of Financial Analysis, Elsevier, vol. 11(1), pages 29-38.
    18. Michael A. Thornton & Marcus J. Chambers, 2013. "Temporal aggregation in macroeconomics," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 13, pages 289-310 Edward Elgar Publishing.
    19. Jun Yu & Peter C.B. Phillips, 2001. "Gaussian Estimation of Continuous Time Models of the Short Term Interest Rate," Cowles Foundation Discussion Papers 1309, Cowles Foundation for Research in Economics, Yale University.
    20. 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.
    21. 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.
    22. Michael A. Thornton & Marcus J. Chambers, 2013. "Continuous-time autoregressive moving average processes in discrete time: representation and embeddability," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 552-561, September.
    23. repec:eee:jmvana:v:157:y:2017:i:c:p:103-114 is not listed on IDEAS

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