Computing Observation Weights for Signal Extraction and Filtering
AbstractWe present algorithms for computing the weights implicitly assigned to observations when estimating unobserved components using a model in state space form. The algorithms are for both filtering and signal extraction. In linear time-invariant models such weights can sometimes be obtained analytically from the Wiener-Kolmogorov formulae. Our method is much more general, being applicable to any model with a linear state space form, including models with deterministic components and time-varying state matrices. It applies to multivariate models and it can be used when there are data irregularities, such as missing observations. The algorithms can be useful for a variety of purposes in econometrics and statistics: (i) the weights for signal extraction can be regarded as equivalent kernel functions and hence the weight pattern can be compared with the kernels typically used in nonparametric trend estimation; (ii) the weight algorithm for filtering implicitly computes the coefficients of the vector error-correction model (VECM) representation of any linear time series model; (iii) as a by-product the mean square errors associated with estimators may be obtained; (iv) the algorithm can be incorporated within a Markov chain Monte Carlo (MCMC) method enabling computation of weights assigned to observations when computing the posterior mean of unobserved components within a Bayesian treatment. A wide range of illustrations show how the algorithms may provide important insights in empirical analysis. The algorithms are provided and implemented for the software package SsfPack 2.3 , that is a set of filtering, smoothing and simulation algorithms for models in state space form (see www.ssfpack.com). Some details of implementation and example programs are given in the appendix of the paper.
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Bibliographic InfoPaper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0888.
Date of creation: 01 Aug 2000
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- Koopman, Siem Jan & Harvey, Andrew, 2003. "Computing observation weights for signal extraction and filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1317-1333, May.
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- Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999.
"Statistical algorithms for models in state space using SsfPack 2.2,"
Royal Economic Society, vol. 2(1), pages 107-160.
- Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper 1998-141, Tilburg University, Center for Economic Research.
- Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers 1998-W06, University of Oxford, Department of Economics.
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1999-44, Tilburg University, Center for Economic Research.
- Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
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