zbMATH — the first resource for mathematics

Exact maximum-likelihood estimation of autoregressive models via the Kalman filter. (English) Zbl 1328.62542
Summary: The pth order autoregression is studied in state-space form, and a closed-form analytic expression is obtained for the unconditional covariance matrix of the initial state vector. It is shown that this covariance matrix depends only on the first \(p\) autocovariances, which makes exact maximum-likelihood estimation via the Kalman filter a straightforward task.

62M20 Inference from stochastic processes and prediction
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
AS 154
Full Text: DOI
[1] Diebold, F.X., The exact initial covariance matrix of the state vector of a general MA(q) process, Economics letters, 22, no. 1, 27-31, (1986) · Zbl 1328.62515
[2] Engle, R.F.; Watson, M., Applications of Kalman filtering in econometrics, World congress of the econometric society, (1985), Cambridge, MA
[3] Gardner, G.; Harvey, A.C.; Phillips, G.D.A., An algorithm for exact maximum likelihood estimation of ARMA models by means of the Kalman filter, Applied statistics, 29, 311-322, (1980) · Zbl 0471.62098
[4] Harvey, A.C., A unified view of statistical forecasting procedures, Journal of forecasting, 3, 245-275, (1984)
[5] Kalman, R.E., A new approach to linear filtering and prediction problems, Journal of basic engineering, 82D, 33-45, (1960)
[6] Nerlove, M.; Grether, D.; Carvalho, J., Analysis of economic time series: A synthesis, (1979), Academic Press New York · Zbl 0473.62077
[7] Schweppe, F.C., Evaluation of likelihood functions for Gaussian signals, IEEE trans. info. theory, 11, 61-70, (1965) · Zbl 0127.10805
[8] Theil, H., Principles of econometrics, (1971), Wiley New York · Zbl 0221.62002
[9] Theil, H.; Goldberger, A.H., On pure and mixed statistical estimation in economics, International economic review, 2, 65-78, (1961)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.