Robust Filtering for Financial Time Series

The sequential inference regarding the state of a system based on new observations is commonly known as the filtering problem. The present work discusses and implements the basic particle filter algorithm of Gordon, Salmond, and Smith (1993) and its robustified counterpart developed by Calvet, Czellar, and Ronchetti (2015). I test the algorithm in simulations and an empirical setting and show that the robustified particle filter performs better than its non-robust counterpart both from a statistical perspective and in terms of numerical stability. I discuss a model for contamination by replacement outliers and show that the performance of the robust particle filter is superior to that of the standard filter in simulations. I apply the algorithm to a time series of daily natural gas futures trading volumes and conclude by highlighting how some existing financial industry applications may benefit from robustification of the model observation density.