Empirical Economics

, Volume 8, Issue 2, pp 71–85 | Cite as

Kalman filtering as an alternative to Ordinary Least Squares — Some theoretical considerations and empirical results

  • P. K. Watson
Article

Abstract

The purpose of this paper is to highlight the superiority of the Kalman filter over Ordinary Least Squares for estimating the unknown coefficients of the classical linear regression model. Both methods are analyzed with respect to their optimality properties and their usefulness in dealing with multicollinearity. Theoretical results are applied to two economic models.

Keywords

Linear Regression Regression Model Theoretical Result Economic Theory Empirical Result 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Athans, M.: The importance of Kalman filtering methods for economic systems. Annals of Economic and Social Measurement,2, 1974, 49–64.Google Scholar
  2. Farrar, D.E., andR.R. Glauber: Multicollinearity in Regression Analysis. The Problem Revisited. Review of Economics and Statistics49, 1967, 92–107.Google Scholar
  3. Frisch, R.: Statistical Confluence Analysis by Means of Complete Regression Systems. Oslo 1934.Google Scholar
  4. Hoerl, A.E., andR.W. Kennard: Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics12 (1), 1970a, 55–67.Google Scholar
  5. —: Ridge Regression: Applications to Nonorthogonal Problems. Technometrics12 (1), 1970b, 69–82.Google Scholar
  6. Jazwinski, A.N.: Stochastic processes and filtering theory. New York 1970.Google Scholar
  7. Johnston, J.: Econometric Methods, 2nd edition. McGraw-Hill 1972.Google Scholar
  8. Kailath, T.: An innovations approach to least squares estimation Part I: Linear filtering in additive noise. IEEE Transactions on Automatic Control, AC-13, 1968, 646–654.Google Scholar
  9. Kalman, R.E.: A new approach to linear filtering and prediction problems. Journal of Basic Engineering,82, 1960, 35–45.Google Scholar
  10. Klein, L.R.: Economic Fluctuations in the U.S., 1921–1941. Chichester 1950.Google Scholar
  11. -: Introduction to Econometrics. Englewood Cliffs 1962.Google Scholar
  12. Mehra, R.K.: On the identification of variances and adaptive Kalman filtering. IEEE Transactions on Automatic Control, AC-15, 1970, 175–184.Google Scholar
  13. Otter, P.W.: The discrete Kalman filter applied to linear regression models: statistical considerations and an application. Statistica Neerlandica,32, 1978, 41–56.Google Scholar
  14. Plackett, R.L.: Some theorems in least Squares. Biometrika37, 1950, 149–157.Google Scholar
  15. Theil, H.: Principles of Econometrics. Amsterdam 1971.Google Scholar
  16. Watson, P.K.: Filtrage dynamique et analyse des séries économiques, Unpublished doctoral thesis, Universite de Paris I (Panthéon-Sorbonne) 1980.Google Scholar

Copyright information

© Physica-Verlag 1983

Authors and Affiliations

  • P. K. Watson
    • 1
  1. 1.Faculty of Social Sciences, Department of EconomicsThe University of the West IndiesSt. Augustine, Trinidad & TobagoWest Indies

Personalised recommendations