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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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Full references

Cited by:
(explanations, 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. Ralph D Snyder, 2005. "A Pedant's Approach to Exponential Smoothing," Monash Econometrics and Business Statistics Working Papers 5/05, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  2. Tommaso Proietti, 2002. "Some Reflections on Trend-Cycle Decompositions with Correlated Components," Econometrics 0209002, EconWPA. [Downloadable!]
    Other versions:
  3. A. C. Harvey & Siem Jan Koopman, 2000. "Computing Observation Weights for Signal Extraction and Filtering," Econometric Society World Congress 2000 Contributed Papers 0888, Econometric Society. [Downloadable!]
    Other versions:
  4. Heather M. Anderson & Chin Nam Low & Ralph Snyder, 2004. "Single Source of Error State Space Approach to the Beveridge Nelson Decomposition," Monash Econometrics and Business Statistics Working Papers 21/04, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  5. Rob J Hyndman & Maxwell L. King & Ivet Pitrun & Baki Billah, 2002. "Local Linear Forecasts Using Cubic Smoothing Splines," Monash Econometrics and Business Statistics Working Papers 10/02, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  6. J Keith Ord & Ralph D Snyder & Anne B Koehler & Rob J Hyndman & Mark Leeds, 2005. "Time Series Forecasting: The Case for the Single Source of Error State Space," Monash Econometrics and Business Statistics Working Papers 7/05, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  7. Tommaso Proietti, 2007. "Band Spectral Estimation for Signal Extraction," CEIS Research Paper 104, Tor Vergata University, CEIS. [Downloadable!]
    Other versions:
  8. Philip Kostov & John Lingard, 2004. "Recurrence analysis techniques for non-stationary and non-linear data," Microeconomics 0409003, EconWPA. [Downloadable!]
  9. Ralph D. Snyder, 2004. "Exponential Smoothing: A Prediction Error Decomposition Principle," Monash Econometrics and Business Statistics Working Papers 15/04, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  10. Charles S. Bos & Neil Shephard, 2004. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Economics Papers 2004-W02, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
    Other versions:
  11. DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics 0660, Faculty of Economics, University of Cambridge. [Downloadable!]
    Other versions:
  12. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0657, Faculty of Economics, University of Cambridge. [Downloadable!]
    Other versions:
  13. Siem Jan Koopman & Charles S. Bos, 2002. "Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series," Tinbergen Institute Discussion Papers 02-113/4, Tinbergen Institute. [Downloadable!]
  14. Tommaso Proietti, 2006. "Measuring Core Inflation by Multivariate Structural Time Series Models," CEIS Research Paper 83, Tor Vergata University, CEIS. [Downloadable!]
  15. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge. [Downloadable!]
  16. Chin Nam Low & Heather Anderson & Ralph Snyder, 2006. "Beveridge-Nelson Decomposition with Markov Switching," Melbourne Institute Working Paper Series wp2006n14, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne. [Downloadable!]
    Other versions:
  17. Thomas B. King, 2005. "Labor productivity and job-market flows: trends, cycles, and correlations," Supervisory Policy Analysis Working Papers 2005-04, Federal Reserve Bank of St. Louis. [Downloadable!]
  18. B. Jungbacker & S.J. Koopman, 2005. "Model-based Measurement of Actual Volatility in High-Frequency Data," Tinbergen Institute Discussion Papers 05-002/4, Tinbergen Institute. [Downloadable!]
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