  A multivariate score-driven filter is developed to extract signals from noisy
vector processes. By assuming that the conditional location vector from a
multivariate Student's t distribution changes over time, we construct a robust
filter which is able to overcome several issues that naturally arise when
modeling heavy-tailed phenomena and, more in general, vectors of dependent
non-Gaussian time series. We derive conditions for stationarity and
invertibility and estimate the unknown parameters by maximum likelihood (ML).
Strong consistency and asymptotic normality of the estimator are proved and the
finite sample properties are illustrated by a Monte-Carlo study. From a
computational point of view, analytical formulae are derived, which consent to
develop estimation procedures based on the Fisher scoring method. The theory is
supported by a novel empirical illustration that shows how the model can be
effectively applied to estimate consumer prices from home scanner data.
