Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-02-02T07:09:46.009Z Has data issue: false hasContentIssue false
  • English
  • Français

The Estimation of Higher-Order Continuous Time Autoregressive Models

Published online by Cambridge University Press:  18 October 2010

A. C. Harvey  and
James H. Stock
A. C. Harvey
Affiliation:
London School of Economics and Harvard University
James H. Stock
Affiliation:
London School of Economics and Harvard University
Get access Rights & Permissions [Opens in a new window]

Abstract

A method is presented for computing maximum likelihood, or Gaussian, estimators of the structural parameters in a continuous time system of higherorder stochastic differential equations. It is argued that it is computationally efficient in the standard case of exact observations made at equally spaced intervals. Furthermore it can be applied in situations where the observations are at unequally spaced intervals, some observations are missing and/or the endogenous variables are subject to measurement error. The method is based on a state space representation and the use of the Kalman–Bucy filter. It is shown how the Kalman-Bucy filter can be modified to deal with flows as well as stocks.

Type
Research Article
Information
Econometric Theory , Volume 1 , Issue 1 , April 1985 , pp. 97 - 117
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. Bergstrom, A. R. (Ed.) (1976). Statistical inference in continuous time economic models. Amsterdam: North Holland, 1976.Google Scholar
2. Bergstrom, A. R. (1983). Gaussian estimation of structural parameters in higher order continuous time dynamic models. Econometrica, 51, 117–152.Google Scholar
3. Chan, S. W., Goodwin, G. C, & Sin, K. W., (1984). Convergence properties of the solution of the Riccati difference equations in optimal filtering of nonstabilizable systems. IEEE Transactions on Automatic Control, AC-29, 110–118.Google Scholar
4. Duncan, D. B., & D., Horn S. (1972). Linear dynamic regression from the viewpoint of regression analysis. Journal of the American Statistical Association, 67, 815–821.Google Scholar
5. Engle, R. F., & Watson, M. (1981). A one-factor multivariate time series model of metropolitan wage rates. Journal of the American Statistical Association 76, 774–781.10.1080/01621459.1981.10477720Google Scholar
6. Gardner, G., Harvey, A. C, & G.D.A, Phillips. An algorithm for exact maximum likelihood estimation of autoregressive-moving average models by means of Kalman filtering. Applied Statistics, 29, 311–322.10.2307/2346910Google Scholar
7. Harvey, A. C. (1981). Time Series Models. Deddington, Oxford: Phillip Allan, and New York: Humanities Press.Google Scholar
8. Jones, R. H. (1981). Fitting a continuous time autoregression to discrete data. In Findley, D. F., (Ed.) Applied Time Series Analysis 11. New York: Academic Press, pp. 651–682.10.1016/B978-0-12-256420-8.50026-5Google Scholar
9. Jones, R. H. (1983). Fitting multivariate models to unequally spaced data. In Parzen, E. (Ed.), Time Series Analysis of Irregular Observations. New York: Springer-Verlag.Google Scholar
10. Kalman, R. E., & Bucy, R. S. (1961). New results in linear filtering and prediction theory. Transactions of the ASME, Series D, Journal of Basic Engineering, 83, 95–108.Google Scholar
11. Phillips, P.C.B. (1974). The estimation of some continuous time models. Econometrica, 42, 803–824.Google Scholar
12. Robinson, P. M. (1976). The estimation of linear differential equations with constant coefficients. Econometrica, 44, 751–764.10.2307/1913441Google Scholar
13. Rosenberg, B. (1973). Random coefficient models: The analysis of a cross section of time series by stochastically convergent parameter regression. Annals of Economic and Social Measurement, 2, 399–428.Google Scholar
14. Wymer, C. R. (1972). Econometric estimation of stochastic differential equation system. Econometrica, 40, 565–577 10.2307/1913185Google Scholar