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Pruned Skewed Kalman Filter and Smoother: With Application to the Yield Curve

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  • Gaygysyz Guljanov
  • Willi Mutschler
  • Mark Trede

Abstract

The Skewed Kalman Filter is a powerful tool for statistical inference of asymmetrically distributed time series data. However, the need to evaluate Gaussian cumulative distribution functions (cdf) of increasing dimensions, creates a numerical barrier such that the filter is usually applicable for univariate models and under simplifying conditions only. Based on the intuition of how skewness propagates through the statespace system, a computationally efficient algorithm is proposed to prune the overall skewness dimension by discarding elements in the cdfs that do not distort the symmetry up to a pre-specified numerical threshold. Accuracy and efficiency of this Pruned Skewed Kalman Filter for general multivariate state-space models are illustrated through an extensive simulation study. The Skewed Kalman Smoother and its pruned implementation are also derived. Applicability is demonstrated by estimating a multivariate dynamic Nelson-Siegel term structure model of the US yield curve with Maximum Likelihood methods. We find that the data clearly favors a skewed distribution for the innovations to the latent level, slope and curvature factors.

Suggested Citation

  • 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.
    • Handle: RePEc:cqe:wpaper:10122
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