Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-17T14:26:57.085Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  11 February 2009

A.R. Bergstrom
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Econometric Theory , Volume 13 , Issue 4 , February 1997 , pp. 467 - 505
Copyright
Copyright © Cambridge University Press 1997

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

Agbeyegbe, T.D. (1984) The exact discrete analog to a closed linear mixed-order system. Journal of Economic Dynamics and Control 7, 363–375.10.1016/0165-1889(84)90025-3CrossRefGoogle Scholar
Bergstrom, A.R. (1983) Gaussian estimation of structural parameters in higher order continuous time dynamic models. Econometrica 51, 117–152.10.2307/1912251CrossRefGoogle Scholar
Bergstrom, A.R. (1984) Continuous time stocha stic models and issues of aggregation over time. In Griliches, Z. & Intriligator, M.D. (eds.), Handbook of Econometrics, pp. 1145–1212. Amsterdam: North-Holland.10.1016/S1573-4412(84)02012-2CrossRefGoogle Scholar
Bergstrom, A.R. (1985) The estimation of parameters in nonstationary higher-order continuous time dynamic models. Econometric Theory 1, 369–385.10.1017/S0266466600011269CrossRefGoogle Scholar
Bergstrom, A.R. (1986) The estimation of open higher-order continuous time dynamic models with mixed stock and flow data. Econometric Theory 2, 350–373.10.1017/S026646660001166XCrossRefGoogle Scholar
Bergstrom, A.R. (1989) Optimal forecasting of discrete stock and flow data generated by a higher order continuous time system. Computers and Mathematics with Applications 17, 1203–1214.10.1016/0898-1221(89)90090-4CrossRefGoogle Scholar
Bergstrom, A.R. (1990) Hypothesis testing in continuous time econometric models. In Bergstrom, A.R., Continuous Time Econometric Modelling, pp. 145–164. Oxford: Oxford University Press.Google Scholar
Bergstrom, A.R., Nowman, K.B., & Wandasiewicz, S. (1994) Monetary and fiscal policy in a secondorder continuous time macroeconometric model of the United Kingdom. Journal of Economic Dynamics and Control 18, 731–761.10.1016/0165-1889(94)90029-9CrossRefGoogle Scholar
Bergstrom, A.R., (Nowman, K.B., & Wymer, C.R. (1992) Gaussian estimation of a second order continuous time macreconometric model of the U.K. Economic Modelling 9, 313–351.Google Scholar
Chambers, M.J. (1991) Estimating general linear continuous time systems. Econometric Theory 1, 531–542.10.1017/S0266466600004758CrossRefGoogle Scholar
Comte, F. (1994) Discrete and Continuous Time Cointegration. Working paper 9442, CREST-INSEE, Paris.Google Scholar
Engle, R.F. & C.Granger, W.J. (1987) Cointegration and error correction: Representation estimation and testing. Econometrica 55, 251–276.10.2307/1913236CrossRefGoogle Scholar
Harvey, A.C., S.G.B. Henry, S. Peters, & Wren-Lewis, S. (1986) Stochastic trends in dynamic regression models: An application to the employment-output equation. Economic Journal 96, 975–985.10.2307/2233168CrossRefGoogle Scholar
Harvey, A.C. & Stock, J.H. (1988) Continuous time autoregressive models with common stochastic trends. Journal of Economic Dynamics and Control 12, 365–384.10.1016/0165-1889(88)90046-2CrossRefGoogle Scholar
Harvey, A.C. & Stock, J.H. (1989) Estimating integrated higher-order continuous time autoregressions with an application to money income causality. Journal of Econometrics 42, 319–336.Google Scholar
Harvey, A.C. & Stock, J.H. (1993) Estimation, smoothing, interpolation, and distribution for structural time-series model in continuous time. In Phillips, P.C.B. (ed.). Models, Methods and Applications of Econometrics, pp. 55–70. Cambridge, MA: Blackwell.Google Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254.10.1016/0165-1889(88)90041-3CrossRefGoogle Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.10.2307/2938278CrossRefGoogle Scholar
Nowman, K.B. (1991) Open higher order continuous time dynamic model with mixed stock and flow data and derivatives of exogenous variables. Econometric Theory 7, 404–408.10.1017/S0266466600004540CrossRefGoogle Scholar
Nowman, K.B. (1992) Computer program for estimation of continuous time dynamic models with mixed stock and flow data. Economic and Financial Computing 1, 25–38.Google Scholar
Phillips, P.C.B. (1974) The estimation of some continuous time models. Econometrica 42, 803–824.10.2307/1913790CrossRefGoogle Scholar
Phillips, P.C.B. (1976) The estimation of linear stochastic differential equations with exogenous variables. In Bergstrom, A.R. (ed.). Statistical Inference in Continuous Time Economic Models, pp. 135–174. Amsterdam: North-Holland.Google Scholar
Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277–302.10.2307/1913237CrossRefGoogle Scholar
Phillips, P.C.B. (1991a) Optimal inference in cointegrated systems. Econometrica 59, 283–306.10.2307/2938258CrossRefGoogle Scholar
Phillips, P.C.B. (1991b) Error correction and long-run equilibrium in continuous time. Econometrica 59, 967–980.10.2307/2938169CrossRefGoogle Scholar
Phillips, P.C.B. (1995) Fully modified least squares and vector autoregression. Econometrica 63, 1023–1079.10.2307/2171721CrossRefGoogle Scholar
Rozanov, Y.A. (1967) Stationary Random Processes. San Francisco: Holden Day.Google Scholar
Simos, T. (1996) Gaussian estimation of a continuous time dynamic model with common stochastic trends. Econometric Theory 12, 361–373.10.1017/S0266466600006630CrossRefGoogle Scholar