A Robust Score-Driven Filter for Multivariate Time Series

TL;DR

This paper introduces a robust score-driven filter for multivariate time series that effectively handles heavy-tailed and dependent non-Gaussian data, with proven theoretical properties and practical application to consumer price estimation.

Contribution

It develops a new score-driven filtering method assuming a time-varying multivariate Student's t distribution, with theoretical guarantees and a practical application.

Findings

The filter is robust to heavy tails and dependence.

Parameters are estimated consistently and asymptotically normally.

Effective application demonstrated on consumer price data.

Abstract

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.