Neural Network Particle Filter for Time Series Data

For the analysis of nonlinear or non‐Gaussian state space models (SSMs), extended Kalman filters and particle filters (PFs) are proposed in the literature. Although these filters allow to formulate SSMs that are much more flexible compared to the linear Gaussian model, they are still based on parametric distributions. In this paper, a novel PF is proposed for the analysis of high‐frequency time series with heavy tails and outliers such as GPS data, road sensor data, climate data, social media data, and data on stock prices. A neural network (NN) is trained using multiple time series to obtain a nonparametric approximation of the probability density function for the observation equation of the SSM and is combined with a PF to obtain estimates for the unobserved states of a local level model. This results in the so‐called neural network particle filter (NNPF). We illustrate the accuracy gains from our proposed method in an extended simulation where time series are generated under the assumption of a local level model and Gaussian, Student's t, noncentral Student's t, and Poisson distributions for the observation equation. The proposed NNPF outperforms existing filters, particularly in the case of continuous distributions with heavy tails and outliers. The proposed NNPF is applied to a real‐life application using vehicle minute counts obtained with road sensors.