Reconstruction of missing data in multivariate processes with applications to causality analysis

Abstract

Recovery of missing observations in time-series has been a century-long subject of study, giving rise to two broad classes of methods, namely, one that reconstructs data and the other that directly estimate the statistical properties of the data, largely for univariate processes. In this work, we present a data reconstruction technique for multivariate processes. The proposed method is developed in the framework of sparse optimization while adopting a parametric approach using vector auto-regressive (VAR) models, where both the temporal and spatial correlations can be exploited for efficient data recovery. The primary purpose of recovering the missing data in this work is to develop a directed graphical or a network representation of the multivariate process under study. Existing methods for data-driven network reconstruction are built on the assumption of data being available at regular intervals. In this respect, the proposed method offers an effective methodology for reconstructing weighted causal networks from missing data. The scope of this work is restricted to linear, jointly stationary multivariate processes that can be suitably represented by VAR models of finite order and missing data of the random type. Simulation studies on different data generating processes with varying proportions of missing observations illustrate the efficacy of the proposed method in recovering the multivariate signals and thereby reconstructing weighted causal networks.