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The Estimation of Parameters in Nonstationary Higher Order Continuous-Time Dynamic Models

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  • Bergstrom, A. R.

Abstract

This paper is concerned with derivation of a new efficient algorithm for computing the exact Gaussian likelihood for structural parameters in nonstationary higher-order continuous-time dynamic models and with its application in the estimation of these parameters. The algorithm completely avoids the computation of the covariance matrix of the observations and is applicable to a system of any order with mixed stock and flow data. It is used as the basis for an iterative procedure in which the structural parameters and the initial state vector are estimated alternately.

Suggested Citation

  • Bergstrom, A. R., 1985. "The Estimation of Parameters in Nonstationary Higher Order Continuous-Time Dynamic Models," Econometric Theory, Cambridge University Press, vol. 1(3), pages 369-385, December.
    • Handle: RePEc:cup:etheor:v:1:y:1985:i:03:p:369-385_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 & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    4. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Wymer Clifford R., 2012. "Continuous-Tme Econometrics of Structural Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-28, April.
    10. Tunaru, Diana, 2017. "Gaussian estimation and forecasting of the U.K. yield curve with multi-factor continuous-time models," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 119-129.
    11. Ramsey, James B., 1996. "On the existence of macro variables and of macro relationships," Journal of Economic Behavior & Organization, Elsevier, vol. 30(3), pages 275-299, September.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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(4), pages 737-774, August.
    18. 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.
    19. 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.
    20. 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.
    21. K. Ben Nowman, 1998. "Continuous-time short term interest rate models," Applied Financial Economics, Taylor & Francis Journals, vol. 8(4), pages 401-407.
    22. 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.
    23. Bhaumik, Prithwish & Ghosal, Subhashis, 2017. "Bayesian inference for higher-order ordinary differential equation models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 103-114.

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