Abstract

Multivariate stochastic volatility (MSV) models, which treat the time-varying covariance matrix of a multivariate time series as a stochastic process, are essential for characterizing dynamic variability and co-dependencies. Existing methods for MSV modeling are largely constrained by the assumption that data are missing at random. However, modern technologies increasingly generate high-dimensional, self-reported time series data in which missingness is inherently informative, limiting the applicability of current approaches. This article develops a novel statistical framework for MSV models with data that are missing not at random. We propose a multivariate imputation method based on a generalized Tukey’s representation that leverages the joint Markovian structure of MSV models to mitigate unidentifiability in informative missingness settings. This imputation approach is integrated into a conditional particle filter with ancestral sampling, implemented within a particle Gibbs sampling scheme to account for imputation uncertainty. The proposed method’s performance is demonstrated through simulation studies and an application to multivariate mobile phone self-reported mood data from an individual monitored following a suicide attempt.