  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.
