A journey from univariate to multivariate functional time series: A comprehensive review

Abstract Functional time series (FTS) analysis has emerged as a potent framework for modeling and forecasting time‐dependent data with functional attributes. In this comprehensive review, we navigate through the intricate landscape of FTS methodologies, meticulously surveying the core principles of univariate FTS and delving into the nuances of multivariate FTS. The journey commences with an exploration of the foundational aspects of univariate FTS analysis. We delve into representation, estimation, and modeling, spotlighting the effectiveness of various parametric and nonparametric models at our disposal. The stage then transitions to multivariate FTS analysis, where we confront the intricacies posed by high‐dimensional data. We explore strategies for dimensionality reduction, forecasting, and the integration of diverse parametric and nonparametric models within the multivariate realm. We also highlight commonly used R packages for modeling and forecasting FTS and multivariate FTS. Acknowledging the dynamic evolution of the field, we dissect challenges and chart future directions, paving a course for refinement and innovation. Through a fusion of multivariate statistics, functional analysis, and time series forecasting, this review underscores the interdisciplinary essence of FTS analysis. It not only reveals past accomplishments, but also illuminates the potential of FTS in unraveling insights and facilitating well‐informed decisions across diverse domains. This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical and Graphical Methods of Data Analysis > Multivariate Analysis