A Randomized Missing Data Approach to Robust Filtering and Forecasting

We put forward a simple new randomized missing data (RMD) approach to robust filtering of state-space models, motivated by the idea that the inclusion of only a small fraction of available highly precise measurements can still extract most of the attainable efficiency gains for filtering latent states, estimating model parameters, and producing out-of-sample forecasts. In our general RMD framework we develop two alternative implementations: endogenous (RMD-N) and exogenous (RMD-X) randomization of missing data. A degree of robustness to outliers and model misspecification is achieved by purposely randomizing over the utilized subset of seemingly highly precise but possibly misspecified or outlier contaminated data measurements in their original time series order, while treating the rest as if missing. Time-series dependence is thus fully preserved and all available measurements can get utilized subject to a degree of downweighting depending on the loss function of interest. The arising robustness-efficiency trade-off is controlled by varying the fraction of randomly utilized measurements or the incurred relative efficiency loss. As an empirical illustration, we show consistently attractive performance of our RMD framework in popular state space models for extracting inflation trends along with model extensions that more directly reflect inflation targeting by central banks.