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Flexible Least Squares for Approximately Linear Systems

Author

Listed:
  • 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://www2.econ.iastate.edu/tesfatsi/flshome.htm

Suggested Citation

  • Kalaba, Robert E. & Tesfatsion, Leigh S., 1990. "Flexible Least Squares for Approximately Linear Systems," Staff General Research Papers Archive 11190, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:11190
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    Cited by:

    1. Claudio Morana, 2005. "The Japanese deflation: has it had real effects? Could it have been avoided?," Applied Economics, Taylor & Francis Journals, vol. 37(12), pages 1337-1352.
    2. 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.
    3. 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.
    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. Evzen Kocenda & Balazs Varga, 2016. "The impact of monetary strategies on inflation persistence," KIER Working Papers 938, Kyoto University, Institute of Economic Research.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Josipa VIŠIC & Blanka ŠKRABIC, "undated". "Determinants of Incoming Cross-Border M&A: Evidence from European Transition Economies," EcoMod2010 259600168, EcoMod.
    11. 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.
    12. Dufour, Jean-Marie & Ghysels, Eric, 1996. "Editors' introduction recent developments in the econometrics of structural change," Journal of Econometrics, Elsevier, vol. 70(1), pages 1-8, January.
    13. A. Talha Yalta, 2016. "Bootstrap Inference of Level Relationships in the Presence of Serially Correlated Errors: A Large Scale Simulation Study and an Application in Energy Demand," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 339-366, August.
    14. 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).
    15. Luis Fernando Melo Velandia & Héctor M. Núñez Amortegui, 2004. "Combinación de pronósticos de la inflación en presencia de cambios estructurales," BORRADORES DE ECONOMIA 002153, BANCO DE LA REPÚBLICA.
    16. He, Ling T., 2001. "Time variation paths of international transmission of stock volatility -- US vs. Hong Kong and South Korea," Global Finance Journal, Elsevier, vol. 12(1), pages 79-93.
    17. Claudio Morana, 2009. "An omnibus noise filter," Computational Statistics, Springer, vol. 24(3), pages 459-479, August.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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