Forecasting observables with particle filters: Any filter will do!

TL;DR

This paper compares various particle filters in state space models, finding that despite efficiency differences, all filters produce nearly identical forecast accuracy, even under model misspecification.

Contribution

It demonstrates that forecast accuracy is invariant to the choice of particle filter, including two new data-driven methods, across simulation and real-world data.

Findings

Filters differ in efficiency and computation time.

Forecast accuracy is nearly identical across filters.

Results hold under model misspecification.

Abstract

We investigate the impact of filter choice on forecast accuracy in state space models. The filters are used both to estimate the posterior distribution of the parameters, via a particle marginal Metropolis-Hastings (PMMH) algorithm, and to produce draws from the filtered distribution of the final state. Multiple filters are entertained, including two new data-driven methods. Simulation exercises are used to document the performance of each PMMH algorithm, in terms of computation time and the efficiency of the chain. We then produce the forecast distributions for the one-step-ahead value of the observed variable, using a fixed number of particles and Markov chain draws. Despite distinct differences in efficiency, the filters yield virtually identical forecasting accuracy, with this result holding under both correct and incorrect specification of the model. This invariance of forecast performance to the specification of the filter also characterizes an empirical analysis of S&P500 daily returns.