A Regularized Kalman Filter (rgKF) for Spiky Data

Serge Darolles (1) , Patrick Duvaut , Emmanuelle Jay

1 DRM - Dauphine Recherches en Management

This chapter presents a new family of algorithms named regularized Kalman Filters (rgKFs) that have been derived to detect and estimate exogenous outliers that might occur in the observation equation of a standard Kalman filter (KF). Inspired from the robust Kalman filter (RKF) of Mattingley and Boyd, which makes use of a l1-regularization step, the authors introduce a simple but efficient detection step in the recursive equations of the RKF. This solution is one means by which to solve the problem of adapting the value of the l1-regularization parameter: when an outlier is detected in the innovation term of the KF, the value of the regularization parameter is set to a value that will let the l1-based optimization problem estimate the amplitude of the spike. The chapter deals with the application of algorithm to detect irregularities in hedge fund returns.

Mots clés: regularized Kalman filter (rgKF); robust Kalman filter (RKF); spiky data

Domaines: Gestion et management

Serge Darolles, Patrick Duvaut, Emmanuelle Jay. A Regularized Kalman Filter (rgKF) for Spiky Data. Multi-factor models and signal processing techniques: application to quantitative finance, pp.117-132, 2013, ⟨10.1002/9781118577387.ch4⟩. ⟨hal-01632887⟩