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Gaussian Estimation of Mixed-Order Continuous-Time Dynamic Models with Unobservable Stochastic Trends from Mixed Stock and Flow Data

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  • Bergstrom, A.R.

Abstract

This paper develops an algorithm for the exact Gaussian estimation of a mixed-order continuous-time dynamic model, with unobservable stochastic trends, from a sample of mixed stock and flow data. Its application yields exact maximum likelihood estimates when the innovations are Brownian motion and either the model is closed or the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under much more general circumstances. The paper includes detailed formulae for the implementation of the algorithm, when the model comprises a mixture of first- and second-order differential equations and both the endogenous and exogenous variables are a mixture of stocks and flows.

Suggested Citation

  • Bergstrom, A.R., 1997. "Gaussian Estimation of Mixed-Order Continuous-Time Dynamic Models with Unobservable Stochastic Trends from Mixed Stock and Flow Data," Econometric Theory, Cambridge University Press, vol. 13(4), pages 467-505, February.
    • Handle: RePEc:cup:etheor:v:13:y:1997:i:04:p:467-505_00
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Russel Cooper & Kieran P. Donaghy, 2000. "Risk and Growth: Theoretical Relationships and Preliminary Estimates for South Africa," Econometric Society World Congress 2000 Contributed Papers 0527, Econometric Society.
    5. Jewitt, Giles & Roderick McCrorie, J., 2005. "Computing estimates of continuous time macroeconometric models on the basis of discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 397-416, April.
    6. Lorenzo Boldrini, 2015. "Forecasting the Global Mean Sea Level, a Continuous-Time State-Space Approach," CREATES Research Papers 2015-40, Department of Economics and Business Economics, Aarhus University.
    7. Chambers, M.J. & McCrorie, J.R., 2004. "Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems," Discussion Paper 2004-40, Tilburg University, Center for Economic Research.
    8. 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.
    9. Joanne S. Ercolani, 2007. "Cyclical Trends in Continuous Time Models," Discussion Papers 07-13, Department of Economics, University of Birmingham.
    10. 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.
    11. Milena Hoyos, 2020. "Mixed First‐ and Second‐Order Cointegrated Continuous Time Models with Mixed Stock and Flow Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 249-267, March.
    12. 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.
    13. Maria Enescu & Marian Enescu, 2009. "Macroeconomic Modeling to Analyze the Development of Investments in Romania in the Transition," Annals of the University of Petrosani, Economics, University of Petrosani, Romania, vol. 9(3), pages 269-276.
    14. McCrorie, J. Roderick & Chambers, Marcus J., 2006. "Granger causality and the sampling of economic processes," Journal of Econometrics, Elsevier, vol. 132(2), pages 311-336, June.
    15. 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.
    16. Michael A. Thornton & Marcus J. Chambers, 2013. "Temporal aggregation in macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 13, pages 289-310, Edward Elgar Publishing.
    17. Chambers, Marcus J. & Roderick McCrorie, J., 2007. "Frequency domain estimation of temporally aggregated Gaussian cointegrated systems," Journal of Econometrics, Elsevier, vol. 136(1), pages 1-29, January.
    18. 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.
    19. 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.

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