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A skewed Kalman filter

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  • Naveau, Philippe
  • Genton, Marc G.
  • Shen, Xilin

Abstract

The popularity of state-space models comes from their flexibilities and the large variety of applications they have been applied to. For multivariate cases, the assumption of normality is very prevalent in the research on Kalman filters. To increase the applicability of the Kalman filter to a wider range of distributions, we propose a new way to introduce skewness to state-space models without losing the computational advantages of the Kalman filter operations. The skewness comes from the extension of the multivariate normal distribution to the closed skew-normal distribution. To illustrate the applicability of such an extension, we present two specific state-space models for which the Kalman filtering operations are carefully described.

Suggested Citation

  • Naveau, Philippe & Genton, Marc G. & Shen, Xilin, 2005. "A skewed Kalman filter," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 382-400, June.
    • Handle: RePEc:eee:jmvana:v:94:y:2005:i:2:p:382-400
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    References listed on IDEAS

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    1. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
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    Cited by:

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    2. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    3. Reinaldo B. Arellano-Valle & Javier E. Contreras-Reyes & Freddy O. López Quintero & Abel Valdebenito, 2019. "A skew-normal dynamic linear model and Bayesian forecasting," Computational Statistics, Springer, vol. 34(3), pages 1055-1085, September.
    4. Gaygysyz Guljanov & Willi Mutschler & Mark Trede, 2022. "Pruned Skewed Kalman Filter and Smoother: With Application to the Yield Curve," CQE Working Papers 10122, Center for Quantitative Economics (CQE), University of Muenster.
    5. Uliha, Gábor, 2016. "Az olajár gyengülő makrogazdasági hatásai. Két versengő elmélet szintézise [Weakening macroeconomic effects of the oil price. A synthesis of two competing theories]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 787-818.
    6. Cabral, Celso Rômulo Barbosa & da-Silva, Cibele Queiroz & Migon, Helio S., 2014. "A dynamic linear model with extended skew-normal for the initial distribution of the state parameter," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 64-80.
    7. Rezaie, Javad & Eidsvik, Jo, 2014. "Kalman filter variants in the closed skew normal setting," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 1-14.
    8. Kim, Hyoung-Moon & Ryu, Duchwan & Mallick, Bani K. & Genton, Marc G., 2014. "Mixtures of skewed Kalman filters," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 228-251.

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