Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-12T04:12:13.550Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  18 October 2010

A. R. Bergstrom
A. R. Bergstrom*
Affiliation:
Universuty of Essex
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Econometric Theory , Volume 1 , Issue 3 , December 1985 , pp. 369 - 385
Copyright
Copyright © Cambridge University Press 1985 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Armington, P. & Wolford, C.. PAC-MOD: An econometric model of selected U.S. and global indicators. World Bank (Global Modeling and Projections Division), Division Working Paper No. 1983–3.Google Scholar
2. Armington, P. & Wolford, C.. Exchange rate dynamics and economic policy. Papers of Armington, Wolford an d Associates, 1984.Google Scholar
3. Basawa, I. V. & Brockwell, P. J.. Asymptotic conditional inference for regular nonergodic models with an application to autoregressive processes. Annals of Statistics 12 (1984): 161–171.10.1214/aos/1176346399Google Scholar
4. Bergstrom, A. R. Non-recursive models as discrete approximations to systems of stochastic differential equations. Econometrica 34 (1966): 173–182.Google Scholar
5. Bergstrom, A. R. Gaussian estimation of structural parameters in higher order continuous time dynamic models. Econometrica 51 (1983): 117–152.Google Scholar
6. Bergstrom, A. R. Continuous time stochastic models and issues of aggregation over time. In Griliches, Z. & Intriligator, M. D. (eds.), Handbook of Econometrics, Chapter 20 and pp. 1145–1212. Amsterdam: North-Holland, 1984.10.1016/S1573-4412(84)02012-2Google Scholar
7. Bergstrom, A. R. Monetary, fiscal and exchange rate policy in a continuous time model of the United Kingdom. In Malgrange, P. and Muet, P. (eds.), Contemporary Macroeconomic Modelling, Chapter 8 and pp. 183–206. Oxford: Blackwell, 1984.Google Scholar
8. Bergstrom, A. R. & Wymer, C. R.. A model of disequilibrium neoclassical growth and its application t o the United Kingdom. In Bergstrom, A. R. (ed.), Statistical Inference in Continuous Time Economic Models, Chapter 10 and pp. 267–327. Amsterdam: North-Holland, 1976.Google Scholar
9. Durbin, J. Efficient fitting of linear models for continuous time stationary time series from discrete data. Bulletin of the International Statistical Institute 38 (1961): 273–282.Google Scholar
10. Gandolfo, G. & Padoan, P. C.. A Disequilibrium Model of Real and Financial Accumulation in an Open Economy. Berlin: Springer, 1984.Google Scholar
11. Hansen, L. P. & Sargent, T. J.. Formulating and estimating continuous time rational expectations models. Federal Reserve Bank of Minneapolis Research Department Staff Report 75, 1981.10.21034/sr.75Google Scholar
12. Harvey, A. C. & Stock, J. H.. The estimation of higher order continuous time autoregressive models. Econometric Theory 1 (1985): 97–117.Google Scholar
13. Jones, R. H. Fitting a continuous time autoregression to discrete data. In Findley, D. F. (ed.), Applied Time Series Analysis II. New York: Academic, 1981.Google Scholar
14. Jonson, P. D., Moses, E. R., & Wymer, C. R.. The RBA76 model of the Australian Economy. In Conference in Applied Economic Research. Reserve Bank of Australia, 1977.Google Scholar
15. Jonson, P. D., McKibbin, W. J., & Trevor, R. G.. Exchange rates and capital flows: A sensitivity analysis. Canadian Journal of Economics 15 (1982): 669–692.10.2307/134921Google Scholar
16. Knight, M. D. & Wymer, C. R.. A macroeconomic model of the United Kingdom. IMF Staff Papers 25 (1978): 742–778.10.2307/3866604Google Scholar
17. Phillips, P. C. B. The structural estimation of a stochastic differential equation system. Econometrica 40 (1972): 1021–1041.Google Scholar
18. Phillips, P. C. B. The estimation of some continuous time models. Econometrica 42 (1974): 803–824.10.2307/1913790Google Scholar
19. Phillips, P. C. B. The estimation of linear stochastic differential equation s with exogenous variables. In Bergstrom, A. R. (ed.), Statistical Inference in Continuous Time Economic Models, Chapter 7 and pp. 135–173. Amsterdam: North-Holland, 1976.Google Scholar
20. Phillips, P. C. B. Some computations based on observed data series of the exogenous variable component of continuous systems. In Bergstrom, A. R. (ed.), Statistical Inference in Continuous Time Economic Models, Chapter 8 and pp. 174–214. Amsterdam: North-Holland, 1976.Google Scholar
21. Phillips, P. C. B. Time series regression with unit roots. Cowles Foundation Discussion Paper No. 740, 1985.Google Scholar
22. Quandt, R. E. Computational problems and methods. In Griliches, Z. and Intriligator, M. D. (eds.), Handbook of Econometrics, Chapter 12 and pp. 699–764. Amsterdam: North-Holland, 1984.Google Scholar
23. Robinson, P. M. Fourier estimation of continuous time models. In Bergstrom, A. R. (ed.), Statistical Inference in Continuous Time Models, Chapter 9 and pp. 215–266. Amsterdam: North-Holland, 1976.Google Scholar
24. Robinson, P. M. The estimation of linear differential equations with constant coefficient. Econometrica 44 (1976): 751–764.10.2307/1913441Google Scholar
25. Robinson, P. M. Instrumental variables estimatio n of differential equations. Econometrica 44 (1976): 765–776.10.2307/1913442Google Scholar
26. Robinson, P. M. The constructio n and estimation of continuous time models and discrete approximations in econometrics. Journal of Econometrics 6 (1977): 173–198.10.1016/0304-4076(77)90014-8Google Scholar
27. Sargan, J. D. Some discrete approximations to continuous time stochastic models. In Bergstrom, A. R. (ed.), Statistical Inference in Continuous Time Economic Models, Chapter 3 and pp. 27–80. Amsterdam: North-Holland, 1976.Google Scholar
28. C., Sassanpour & Sheen., J. An empirical analysis of the effect of monetary disequilibrium in open economies. Journal of Monetary Economics 13 (1984): 127–163.Google Scholar
29. Tussio, G. Demand management and exchange rate policy: the Italian experience. IMF Staff Papers 28 (1981): 80–117.Google Scholar
30. Whittle, P. Hypothesis Testing in Time Series Analysis. Stockholm: Almqvist and Wicksell, 1951.Google Scholar
31. Whittle, P. The analysis of multiple stationary time series. Journal of the Royal Statistical Society, Series B 15 (1953): 125–139.Google Scholar
32. Wymer, C. R. Econometric estimation of stochastic differential equation systems. Econo-metrica 40 (1972): 565–577.Google Scholar
33. Wymer, C. R. Computer Programs, International Monetary Fund, 1978.10.5089/9781616351908.011Google Scholar