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Identification and Estimation of Continuous Time Dynamic Systems With Exogenous Variables Using Panel Data

Published online by Cambridge University Press:  11 February 2009

Alfred Hamerle ,
Hermann Singer  and
Willi Nagl
Alfred Hamerle
Affiliation:
University of Regensburg
Hermann Singer
Affiliation:
University of Regensburg
Willi Nagl
Affiliation:
University of Konstanz
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Abstract

This paper deals with the identification and maximum likelihood estimation of the parameters of a stochastic differential equation from discrete time sampling. Score function and maximum likelihood equations are derived explicitly. The stochastic differential equation system is extended to allow for random effects and the analysis of panel data. In addition, we investigate the identifiability of the continuous time parameters, in particular the impact of the inclusion of exogenous variables.

Type
Miscellanea
Information
Econometric Theory , Volume 9 , Issue 2 , April 1993 , pp. 283 - 295
Copyright
Copyright © Cambridge University Press 1993

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References

1.Arnold, L.Stochastic Differential Equations. New York: Wiley, 1974.Google Scholar
2.Bergstrom, A.R.Non-recursive models as discrete approximations to systems of stochastic differential equations. Econometrica 34 (1966): 173–182.CrossRefGoogle Scholar
3.Bergstrom, A.R.The Construction and Use of Economic Models. London: English Universities Press, 1967.Google Scholar
Bergstrom, A.R. (ed.), Statistical Inference in Continuous Time Economic Models. Amsterdam: North-Holland, 1976.Google Scholar
5.Bergstrom, A.R.Gaussian estimation of structural parameters in higher continuous time dynamic models. Econometrica 51 (1983): 117–152.CrossRefGoogle Scholar
Bergstrom, A.R. Continuous time stochastic models and issues of aggregation over time. In Griliches, Z. and Intrilligator, M.D. (eds.), Handbook of Econometrics, Vol. II. Amsterdam: North-Holland, 1984.Google Scholar
7.Bergstrom, A.R.The estimation of parameters in nonstationary higher-order continuous-time dynamic models. Econometric Theory 1 (1985): 369–385.CrossRefGoogle Scholar
8.Bergstrom, A.R.The history of continuous-time econometric models. Econometric Theory 4 (1988): 365–383.CrossRefGoogle Scholar
9.Bergstrom, A.R.Continuous Time Econometric Modelling. Oxford: Oxford University Press, 1990.Google Scholar
10.Dennis, J.E. Jr. & Schnabel, R.B.. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Englewood Cliffs; NJ: Prentice-Hall, 1983.Google Scholar
11.Gandolfo, G.Qualitative Analysis and Econometric Estimation of Continuous Time Dynamic Models. Amsterdam: North-Holland, 1981.Google Scholar
12.Hansen, L.P. & Sargent, T.J.. The dimensionality of the aliasing problem in models with rational spectral densities. Econometrica 51 (1983): 377–387.CrossRefGoogle Scholar
13.Harvey, A.C. & Stock, J.H.. The estimation of higher-order continuous time autoregressive models. Econometric Theory 1 (1985): 97–117.CrossRefGoogle Scholar
14.Hsiao, C.Analysis of Panel Data. Cambridge: Cambridge University Press, 1986.Google Scholar
Jones, R.H. Fitting multivariate models to unequally spaced data. In Parzen, E. (ed.), Time Series Analysis of Irregularly Observed Data. New York: Springer, 1984.Google Scholar
16.Jones, R.H. & Tryon, P.V.. Continuous time series models for unequally spaced data applied to modeling atomic clocks. SIAM Journal of Scientific Statistical Computing 8 (1987): 71–81.CrossRefGoogle Scholar
17.Jones, R.H. & Ackerson, L.M.. Serial correlation in unequally spaced longitudinal data. Biometrika 77 (1990): 721–731.CrossRefGoogle Scholar
18.Magnus, J.R. & Neudecker, H.. Matrix Differential Calculus with Applications in Statistics and Econometrics. Chichester: Wiley, 1988.Google Scholar
19.McDonald, R.P. & Swaminathan, H.. A simple matrix calculus with applications to multivariate analysis. General Systems XVIII (1973): 37–54.Google Scholar
20.Phillips, P.C.B.The structural estimation of a stochastic differential equation system. Econometrica 40 (1972): 1021–1041.CrossRefGoogle Scholar
21.Phillips, P.C.B.The problem of identification in finite parameter continuous time models. Journal of Econometrics 1 (1973): 351–362.CrossRefGoogle Scholar
22.Phillips, P.C.B.The estimation of some continuous time models. Econometrica 42 (1974): 803–824.CrossRefGoogle Scholar
Phillips, P.C.B. The estimation of linear stochastic differential equations with exogenous variables. In Bergstrom, A.R. (ed.), Statistical Inference in Continuous Time Economic Models, pp. 135–173. Amsterdam: North-Holland, 1976.Google Scholar
24.Robinson, P.M.The estimation of linear differential equations with constant coefficients. Econometrica 44 (1976): 751–764.CrossRefGoogle Scholar
25.Robinson, P.M.Instrumental variables estimation of differential equations. Econometrica 44 (1976): 765–776.CrossRefGoogle Scholar
26.Robinson, P.M.The construction and estimation of continuous time models and discrete approximations in econometrics. Journal of Econometrics 6 (1977): 173–198.CrossRefGoogle Scholar
Robinson, P.M. Continuous model fitting from discrete data. In Brillinger, D.R. and Tiao, G.C. (eds.), Directions in Time Series. Ames: Iowa State University, 1978.Google Scholar
Sargan, J.D. Some discrete approximations to continuous time stochastic models. In Bergstrom, A.R. (ed.), Statistical Inference in Continuous Time Economic Models, pp. 27–80. Amsterdam: North-Holland, 1976.Google Scholar
29.Singer, H.Parameterschätzung in Zeitkontinuierlichen Dynamischen Systemen. Konstanz: Hartung-Gorre, 1990.Google Scholar
30.Singer, H.LSDE – A Program Package for the Simulation, Graphical Display, Optimal Filtering and Maximum Likelihood Estimation of Linear Stochastic Differential Equations, User's Guide. Meersburg: Author, 1991.Google Scholar
31.Singer, H.Continuous-time dynamical systems with sampled data, errors of measurement and unobserved components. Journal of Time Series Analysis (1993), forthcoming.CrossRefGoogle Scholar
32.Wymer, C.R.Econometric estimation of stochastic differential equation systems. Econometrica 40 (1972): 565–577.CrossRefGoogle Scholar
33.Zadrozny, P.Gaussian likelihood of continuous time ARMAX models when data are stocks and flows at different frequencies. Econometric Theory 4 (1988): 108–124.CrossRefGoogle Scholar