  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 data measurements in their original
time series order, while treating the rest as if missing. The arising
robustness-efficiency trade-off is controlled by varying the fraction of
randomly utilized measurements. Our RMD framework thus relates to but is
different from a wide range of machine learning methods trading off bias
against variance. It also provides a time-series extension of bootstrap
aggregation (bagging). As an empirical illustration, we show consistently
attractive performance of RMD filtering and forecasting in popular state space
models for extracting inflation trends known to be hindered by measurement
outliers.
