IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v16y2012i2n8.html
   My bibliography  Save this article

Continuous-Tme Econometrics of Structural Models

Author

Listed:
  • Wymer Clifford R.

    () (Sapienza University of Rome)

Abstract

Much of economic theory, especially macro-economics and the study of commodity, financial, and other markets, relies on the use of non-linear structural models to study medium-term and long-run dynamic behaviour of an economy. Continuous-time econometrics is based on the argument that as economic systems are largely continuous they can be better represented and estimated by differential equation rather than difference equation systems. This paper reviews the development of full-information Gaussian estimators of non-linear systems which may then be extended to the estimation of models of intertemporally optimizing agents and other boundary point models, and models where the parameters of the stochastic innovation process enter the deterministic part of the model or vice versa. The long-properties of these models may be studied by calculating the Lyapunov exponents which give information on the form of the attractor the model, the dynamic stability of the model for given parameter values and whether it is structurally stable. The critical dependence of some attractors, and particularly strange attractors, on parameter values emphasizes the need for consistent, efficient estimation. A structural approach provides a rigorous alternative to using single time series to determine whether economic systems exhibit aperiodic or chaotic dynamical behavior.

Suggested Citation

  • Wymer Clifford R., 2012. "Continuous-Tme Econometrics of Structural Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-28, April.
  • Handle: RePEc:bpj:sndecm:v:16:y:2012:i:2:n:8
    DOI: 10.1515/1558-3708.1936
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/1558-3708.1936
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Peter M Robinson, 2001. "The Memory of Stochastic Volatility Models," STICERD - Econometrics Paper Series 410, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Nowman, K B, 1997. "Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 52(4), pages 1695-1706, September.
    4. 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(3), pages 350-373, December.
    5. Daniela Federici & Giancarlo Gandolfo, 2011. "The Euro/Dollar Exchange Rate: Chaotic or Non-Chaotic?," CESifo Working Paper Series 3420, CESifo.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    7. Gandolfo, Giancarlo & Padoan, Pietro Carlo, 1990. "The Italian continuous time model : Theory and empirical results," Economic Modelling, Elsevier, vol. 7(2), pages 91-132, April.
    8. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    9. 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.
    10. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    11. Gianfranco Piras & Kieran Donaghy & Giuseppe Arbia, 2007. "Nonlinear regional economic dynamics: continuous-time specification, estimation and stability analysis," Journal of Geographical Systems, Springer, vol. 9(4), pages 311-344, December.
    12. Phillips, P C B, 1991. "Error Correction and Long-Run Equilibrium in Continuous Time," Econometrica, Econometric Society, vol. 59(4), pages 967-980, July.
    13. Russel Cooper & Kieran Donaghy & Geoffrey Hewings (ed.), 2007. "Globalization and Regional Economic Modeling," Advances in Spatial Science, Springer, number 978-3-540-72444-5.
    14. Wymer, Clifford R., 2009. "Aperiodic Dynamics In The Bergstrom/Wymer Model Of The United Kingdom," Econometric Theory, Cambridge University Press, vol. 25(4), pages 1099-1111, August.
    15. Wymer, Clifford R., 1997. "Structural Nonlinear Continuous-Time Models In Econometrics," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 518-548, June.
    16. Robinson, P. M., 2001. "The memory of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 101(2), pages 195-218, April.
    17. Pindyck, Robert S, 1978. "The Optimal Exploration and Production of Nonrenewable Resources," Journal of Political Economy, University of Chicago Press, vol. 86(5), pages 841-861, October.
    18. Robinson, Peter M., 2001. "The memory of stochastic volatility models," LSE Research Online Documents on Economics 2298, London School of Economics and Political Science, LSE Library.
    19. Barnett, William A. & He, Yijun, 2002. "Stabilization Policy As Bifurcation Selection: Would Stabilization Policy Work If The Economy Really Were Unstable?," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 713-747, November.
    20. Saltari Enrico & Wymer Clifford R. & Federici Daniela & Giannetti Marilena, 2012. "Technological Adoption with Imperfect Markets in the Italian Economy," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-30, April.
    21. Bergstrom, Albert Rex, 1983. "Gaussian Estimation of Structural Parameters in Higher Order Continuous Time Dynamic Models," Econometrica, Econometric Society, vol. 51(1), pages 117-152, January.
    22. Amitrajeet A Batabyal & Peter Nijkamp (ed.), 2011. "Research Tools in Natural Resource and Environmental Economics," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7496, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 684-700, November.
    5. Wilfredo Palma & Mauricio Zevallos, 2004. "Analysis of the correlation structure of square time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 529-550, July.
    6. 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.
    7. 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.
    8. 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.
    9. K. Ben Nowman, 1998. "Continuous-time short term interest rate models," Applied Financial Economics, Taylor & Francis Journals, vol. 8(4), pages 401-407.
    10. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2015. "The impact of financial crises on the risk–return tradeoff and the leverage effect," Economic Modelling, Elsevier, vol. 49(C), pages 407-418.
    11. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameterfor nonlinear time series," STICERD - Econometrics Paper Series 497, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    12. 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.
    13. Federici, Daniela & Saltari, Enrico, 2018. "Elasticity Of Substitution And Technical Progress: Is There A Misspecification Problem?," Macroeconomic Dynamics, Cambridge University Press, vol. 22(1), pages 101-121, January.
    14. David Mcmillan & Alan Speight, 2008. "Long-memory in high-frequency exchange rate volatility under temporal aggregation," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 251-261.
    15. 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.
    16. Dahl Christian M & Iglesias Emma, 2011. "Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-32, February.
    17. 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.
    18. da Silva, Afonso Gonçalves & Robinson, Peter M., 2008. "Fractional Cointegration In Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1207-1253, October.
    19. 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.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:sndecm:v:16:y:2012:i:2:n:8. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla). General contact details of provider: https://www.degruyter.com .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.