Reconstructing the Kalman Filter for Stationary and Non Stationary Time Series
AbstractA Kalman filter, suitable for application to a stationary or a non-stationary time series, is proposed. It works on time series with missing values. It can be used on seasonal time series where the associated state space model may not satisfy the traditional observability condition. A new concept called an 'extended normal random vector' is introduced and used throughout the paper to simplify the specification of the Kalman filter. It is an aggregate of means, variances, covariances and other information needed to define the state of a system at a given point in time. By working with this aggregate, the algorithm is specified without direct recourse to those relatively complex formulae for calculating associated means and variances, normally found in traditional expositions of the Kalman filter. A computer implementation of the algorithm is also described where the extended normal random vector is treated as an object; the operations of addition, subtraction and multiplication are overloaded to work on instances of this object; and a form of statistical conditioning is implemented as an operator.
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Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 14/02.
Length: 31 pages
Date of creation: Oct 2002
Date of revision:
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Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Web page: http://www.buseco.monash.edu.au/depts/ebs/
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Other versions of this item:
- Snyder Ralph D & Forbes Catherine S, 2003. "Reconstructing the Kalman Filter for Stationary and Non Stationary Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(2), pages 1-20, July.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-10-23 (All new papers)
- NEP-ECM-2002-10-23 (Econometrics)
- NEP-ETS-2002-10-23 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Koopman, S.J.M. & Durbin, J., 1998. "Fast Filtering and Smoothing for Multivariate State Space Models," Discussion Paper 1998-18, Tilburg University, Center for Economic Research.
- Rob Hyndman & Muhammad Akram & Blyth Archibald, 2008. "The admissible parameter space for exponential smoothing models," Annals of the Institute of Statistical Mathematics, Springer, vol. 60(2), pages 407-426, June.
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