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A Quadratic Kalman Filter

Author

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  • Monfort, Alain
  • Renne, Jean-Paul
  • Roussellet, Guillaume
Abstract
We propose a new filtering and smoothing technique for non-linear state-space models. Observed variables are quadratic functions of latent factors following a Gaussian VAR. Stacking the vector of factors with its vectorized outer-product, we form an augmented state vector whose first two conditional moments are known in closed-form. We also provide analytical formulae for the unconditional moments of this augmented vector. Our new Quadratic Kalman Filter (Qkf) exploits these properties to formulate fast and simple filtering and smoothing algorithms. A simulation study first emphasizes that the Qkf outperforms the extended and unscented approaches in the filtering exercise showing up to 70% RMSEs improvement of filtered values. Second, it provides evidence that Qkf-based maximum-likelihood estimates of model parameters always possess lower bias or lower RMSEs than the alternative estimators.

Suggested Citation

  • Monfort, Alain & Renne, Jean-Paul & Roussellet, Guillaume, 2015. "A Quadratic Kalman Filter," Journal of Econometrics, Elsevier, vol. 187(1), pages 43-56.
    • Handle: RePEc:eee:econom:v:187:y:2015:i:1:p:43-56
    DOI: 10.1016/j.jeconom.2015.01.003
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    2. Xi Kleisinger-Yu & Vlatka Komaric & Martin Larsson & Markus Regez, 2019. "A multi-factor polynomial framework for long-term electricity forwards with delivery period," Papers 1908.08954, arXiv.org, revised Jun 2020.
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    6. Dubecq, Simon & Monfort, Alain & Renne, Jean-Paul & Roussellet, Guillaume, 2016. "Credit and liquidity in interbank rates: A quadratic approach," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 29-46.

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    More about this item

    Keywords

    Non-linear filtering; Non-linear smoothing; Quadratic model; Kalman filter; Quasi maximum likelihood;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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