An economist's guide to the Kalman filter

Authors

  • Francisco Venegas Universidad Nacional Autónoma de México
  • Enrique De Alba Instituto Tecnológico Autónomo de México
  • Manuel Ordorica El Colegio de México

DOI:

https://doi.org/10.24201/ee.v10i2.268

Keywords:

Kalman Filter, KF, information theory, Bayesian inference

Abstract

Almost since its appearance, the Kalman Filter (KF) has been successfully used in control engineering. Unfortunately, most of its important results have been published in engineering journals with language, notation and style proper of engineers. In this paper, we want to present the KF in an attractive way to economists by using information theory and Bayesian inference.

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References

Akaike, H. (1981). "Likelihood of a Model and Information Criteria", Journal of Econometrics, 16, pp. 3-14.

Athans, M. (1974). "The Importance of Kalman Filtering Methods for Economic System", Annals of Economics and Social Measurements, 3, pp. 49-74.

Basar, T., and M. Salmon (1989). "On the Convergence of Beliefs and Policy to a Rational Expectations Equilibrium in a Dual Policy Problem", in W. Marois, A. Soubeyran, and D. Laussel (eds.), Issues in Monetary Economics, Springer Verlag, pp. 207-223.

Bellman, R. (1957). Dynamic Programming, Princeton, Princeton University Press.

Burmeister, E., K. D. Wall, and J.D. Hamilton (1982). "Kalman Filtering Estimations of Unobserved Rational Expectations with one Application to the German Hyperinflation", Journal of Econometrics, 20, pp. 255-284.

Burmeister E. and J. D. Hamilton (1986). "Estimations of Unobserved Expected Monthly Inflation Using Kalman Filtering", Journal of Business and Economic Statistics, 4, pp. 147-160.

Cagan, P. (1956). "The Monetary Dynamics of Hyperinflation", in M. Friedman, (ed.), Studies in the Quantity Theory of Money, University of Chicago Press.

Calvo, G. A. (1991). "Temporary Stabilization Policy: The Case of Flexible Prices and Exchange Rates", Journal of Economic Dynamics and Control, 15, pp. 197-213.

Cooley, T., and E. Prescott (1973). "Varying Parameter Regression. A Theory and Some Applications", Annals of Economic and Social Measurement, 2, pp. 463-474.

Cozzolino, J. M., and M. J. Zahner (1973). "The Maximum-Entropy Distribution of the Future Market Price of Stock", Operations Research, 21, pp. 1200-1211.

Hamilton, J. D. (1994). Time Series Analysis, Princeton University Press.

Harvey, A., and G. Phillips (1982). "Estimation of Regression Models with Time Varying Parameters", in M. Deistler, E. Furst, and G. Schwodiauer (eds.), Games, Economic Dynamics and Time Series Analysis, Physica-Verlag, Wien-Wurzburg, pp. 306-321.

Hildreth, C, and J. P. Houck (1968). "Some Estimators for a Linear Model with Random Coefficients", JASA, 63, pp. 584-595.

Ho, Y. C, and R. C. K. Lee (1964). "A Bayesian Approach to Problems in Stochastic Estimation and Control", IEEE Trans. Automat. Contr., AC-9, pp. 333-339.

Jaynes, E. T. (1957). "Information Theory and Statistical Mechanics 1", Phys. Rev., 106, pp. 620-630.

Kalman, R. E. (1960). "A New Approach to Linear Filtering and Prediction Problems", Transactions ASME, Series D. J. of Basic Engineering, 82, pp. 35-45.

Kalman, R. E. and R. Bucy (1961). "New Results in Linear Filtering and Prediction Theory", Transactions ASME, Series D. J. of Basic Engineering, 83, pp. 95-108.

Kapur, J. N. (1990). "Maximum Entropy Models in Science and Engineering", John Wiley, pp. 593-602.

Lucas, R. E., Jr. (1973). "Some International Evidence on Output-Inflation Tradeoffs", American Economic Review, 63, pp. 326-334.

Lucas, R. E., Jr. (1976). Econometric Policy Evaluation. A Critique, in K. Brunner and A. Meltzer (eds.), The Phillips Curve and the Public Policy, vol. 1 of Carnegie-Rochester Conference in Public Policy, a supplementation series to the Journal of Monetary Economics, Amsterdam, North Holland Publishers.

Meditch, J. S. (1969). Stochastic Optimal Linear Estimation and Control, New York, McGraw Hill.

Meinhold, R. J., and N. D. Singpurwalla (1983). "Understanding the Kalman Filter", The American Statistician, 37, pp. 123-127.

Muth, J. F. (1961). "Rational Expectations and the Theory of Price Movements", Econometrica, 29, pp. 315-335.

Sargent, T. J. (1989). "Two Models of Measurements and the Investment Accelerator", Journal of Political Economy, 97, pp. 251-287.

Sorenson H. W. (1985). Kalman Filtering: Theory and Applications, Selected Reprint Series, IEEE Press.

Stratonovich, R. L. (1960). "Applications of the Theory of Markoff Processes in Optimal Signal Detection", Radio Eng. Electron. Phys., 1, pp. 1-19.

Swamy, P. A. V. B., and J. S. Mehta (1975). "Bayesian and Non-Bayesian Analysis of Switching Regressions and of Random Coefficient Regression Models", JASA, 70, pp. 593-602.

Swerling, P. (1959). "First Order Error Propagation in a Stagewise Smoothing Procedure for Satellite Observations", Journal Astronautical Sci., 6, pp. 46-52.

Tabellini, G. (1986). "Money, Debt and Deficits in a Dynamic Game", Journal of Economic Dynamics and Control, 10, pp. 427-442.

Theil, H., M. Scholes, and P. Uribe (1965). An Informational Approach to the Measurement of Industrial Concentration, Report 6512, Center for Mathematical Studies in Business and Economics, The University of Chicago.

Theil, H., and P. Uribe (1965). The Information Approach to the Aggregation of Input-Output Tables, Report 6503 Center for Mathematical Studies in Business and Economics, The University of Chicago.

Uribe, P., C. G. De Leeuw, and H. Theil (1965). The Informational Approach to the Prediction of Interregional Trade Flows, Report 6507, Econometric Institute of the Netherlands School of Economics.

Venegas, F. (1990). "On Regularity and Optimality Conditions for Maximum Entropy Priors", Brazilian Journal of Probability and Statistics, 4, pp. 105-136.

Venegas, F. (1990a). "Información suplementaria a priori, aspectos computacionales y clasificación", Estadística, IASI, 42, no. 139, Interamerican Institute of Statistics, pp. 64-80. Also available in Contributions to Probability and Mathematical Statistics, Acts of the IV Latin-American Meeting in Probability and Mathematical Statistics, México City, 1990, pp. 228-237.

Venegas, F., and E. de Alba (1992). Aprendizaje sobre utilidad a través de la optimización de medidas de información, Recent Advances in Bayesian Statistics and Econometrics, Caracas, Venezuela.

Venegas, F. (1992a). "Entropy Maximization and Cross-Entropy Minimization: A Matriz Approach", Agrociencia, Serie Matemáticas Aplicadas, Estadística y Computación, 2, No. 3, pp. 71-77.

Venegas, F. (1992b). On Optimal Production Planning under a Randomly Disturbated Demand, IV Latin-Ibero-American Meeting on Operations Research and Systems Engineering, Mexico City.

Venegas, F. (1993). On Optimal Production-Inventory Policies for a Multiple-Plant Firm with Correlated Demands, XII Latin-American Meeting of the Econometric Society, Tucumán, Argentina.

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Published

1995-07-01

How to Cite

Venegas, F., De Alba, E., & Ordorica, M. (1995). An economist’s guide to the Kalman filter. Estudios Económicos De El Colegio De México, 10(2), 123–145. https://doi.org/10.24201/ee.v10i2.268
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20-vol. 10, no. 2, july-december, 1995

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