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Flexible Least Squares for Approximately Linear Systems

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Author Info

  • Kalaba, Robert E.
  • Tesfatsion, Leigh S.

Abstract

The problem of filtering and smoothing for a system described by approximately linear dynamic and measurement relations has been studied for many decades. Yet the potential problem of misspecified dynamics, which makes the usual probabilistic assumptions involving normality and independence questionable at best, has not received the attention it merits. This study proposes a probability-free filter that meets this misspecification problem head on, referred to as Generalized Flexible Least Squares for Approximately Linear Systems (GFLS-ALS). A Fortran program implementation is provided for GFLS-ALS, and references to simulation and empirical results are given. Although GFLS-ALS has close connections with the standard Kalman filter, it is concretely demonstrated that there are also important conceptual and computational distinctions. The Kalman filter provides a unique estimate for the state sequence, conditional on maintained probability assumptions for discrepancy terms. In contrast, the GFLS-ALS filter provides a family of state sequence estimates, each of which is vector-minimally incompatible with the prior dynamical and measurement specifications. The GFLS-ALS filter was incorporated into the statistical package GAUSS/TSM in 1997.Annotated pointers to related work can be accessed at http://www.econ.iastate.edu/tesfatsi/flshome.htm

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Bibliographic Info

Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 11190.

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Date of creation: 01 Jan 1990
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Publication status: Published in IEEE Transactions on Systems, Man, and Cybernetics 1990, vol. 20 no. 5, pp. 978-989
Handle: RePEc:isu:genres:11190

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
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Web page: http://www.econ.iastate.edu
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Cited by:
  1. Vêlayoudom Marimoutou & Denis Peguin & Anne Peguin-Feissolle, 2009. "The "distance-varying" gravity model in international economics: is the distance an obstacle to trade?," Economics Bulletin, AccessEcon, vol. 29(2), pages 1139-1155.
  2. Zsolt Darvas & Balázs Varga, 2014. "Inflation persistence in central and eastern European countries," Applied Economics, Taylor & Francis Journals, vol. 46(13), pages 1437-1448, May.
  3. Ling T. He, & James. R. Webb & Neil Myer, 2003. "Interest Rate Sensitivities of REIT Returns," International Real Estate Review, Asian Real Estate Society, vol. 6(1), pages 1-21.
  4. He, Ling T., 2005. "Instability and predictability of factor betas of industrial stocks: The Flexible Least Squares solutions," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 619-640, September.
  5. Kalaba, Robert & Tesfatsion, Leigh, 1996. "A multicriteria approach to model specification and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 21(2), pages 193-214, February.
  6. Lutkepohl, Helmut & Herwartz, Helmut, 1996. "Specification of varying coefficient time series models via generalized flexible least squares," Journal of Econometrics, Elsevier, vol. 70(1), pages 261-290, January.
  7. Claudio Morana, 2009. "An omnibus noise filter," Computational Statistics, Springer, vol. 24(3), pages 459-479, August.
  8. Luis Fernando Melo & Héctor Núñez, . "Combinación de Pronósticos de la Inflación en Presencia de cambios Estructurales," Borradores de Economia 286, Banco de la Republica de Colombia.
  9. Zsolt Darvas & Balázs Varga, 2012. "Uncovering Time-Varying Parameters with the Kalman-Filter and the Flexible Least Squares: a Monte Carlo Study," Working Papers 1204, Department of Mathematical Economics and Economic Analysis, Corvinus University of Budapest.
  10. Zsuzsanna Zsibók & Balázs Varga, 2012. "Inflation Persistence in Hungary: a Spatial Analysis," Working Papers 1203, Department of Mathematical Economics and Economic Analysis, Corvinus University of Budapest.
  11. Claudio Morana, 2004. "The Japanese Deflation: Has It Had Real Effects? Could It Have Been Avoided?," ICER Working Papers 29-2004, ICER - International Centre for Economic Research.
  12. Kuethe, Todd H. & Foster, Kenneth A. & Florax, Raymond J.G.M., 2008. "A Spatial Hedonic Model with Time-Varying Parameters: A New Method Using Flexible Least Squares," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6306, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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