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Signal extraction and the formulation of unobserved components models

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Author Info
ANDREW HARVEY
SIEM JAN KOOPMAN

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Abstract

This paper looks at unobserved components models and examines the implied weighting patterns for signal extraction. There are four main themes. The first concerns the implications of correlated disturbances driving the components, especially those cases in which the correlation is perfect. The second is about the way in which ARIMA-based methods for trend extraction relate to those based on unobserved components. The third explores the impact of heteroscedasticity and irregular spacing and shows how setting up models with t -distributed disturbances leads to weighting patterns which are robust to outliers and breaks. Finally, a comparison is made between implied weighting patterns with kernels used in non-parametric trend estimation and equivalent kernels used in spline smoothing. It is demonstrated that with irregularly spaced data, the weighting used by conventional spline smoothing techniques is not the same as that obtained from the time series model based approach.

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Publisher Info
Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 3 (2000)
Issue (Month): 1 ()
Pages: 84-107
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Handle: RePEc:ect:emjrnl:v:3:y:2000:i:1:p:84-107

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Related research
Keywords: Cubic splines; Kalman filter and smoother; Kernels; Robustness; Structural time series model; Trend; Wiener–Kolmogorov filter.;

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References listed on IDEAS
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.:
  1. 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. [Downloadable!] (restricted)
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  2. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September. [Downloadable!] (restricted)
  3. Durbin, J. & Koopman, S.J., 1998. "Time series analysis of non-gaussian observations based on state space models from both classical and bayesian perspectives," Discussion Paper 142, Tilburg University, Center for Economic Research. [Downloadable!]
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  4. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept. [Downloadable!] (restricted)
  5. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July. [Downloadable!] (restricted)
  6. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
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  7. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  8. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
  9. Peter Burridge & Kenneth Wallis, 1988. "Prediction theory for autoregressivemoving average processes," Econometric Reviews, Taylor and Francis Journals, vol. 7(1), pages 65-95. [Downloadable!] (restricted)
  10. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, vol. 67(2), pages 139-146, May. [Downloadable!] (restricted)
  11. I. Gijbels & A. Pope & M. P. Wand, 1999. "Understanding exponential smoothing via kernel regression," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 39-50. [Downloadable!] (restricted)
  12. Koopman, S.J. & Shephard, N. & Doornik, J.A., 1998. "Statistical algorithms for models in state space using ssfpack 2.2," Discussion Paper 141, Tilburg University, Center for Economic Research. [Downloadable!]
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