A Quadratic Kalman Filter

作者：Monfort Alain; Renne Jean Paul; Roussellet Guillaume^*

来源：Journal of Econometrics, 2015, 187(1): 43-56.

DOI：10.1016/j.jeconom.2015.01.003

• Non-linear filtering
• Non-linear smoothing
• Quadratic model
• Kalman filter
• Quasi maximum likelihood

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.

• 出版日期2015-7