Over the Stability Space of a Multivariate Time Series

This paper jointly addresses the challenges of non-stationarity and high dimensionality in analysing multivariate time series. Building on the classical concept of cointegration, we introduce a more flexible notion, called stability space, aimed at capturing stationary components in settings where traditional assumptions may not hold. Based on the dimensionality reduction techniques of Partial Least Squares and Principal Component Analysis, we proposed two non-parametric procedures for estimating such a space and a targeted selection of components that prioritises stationarity. We compare these alternatives with the parametric Johansen procedure, when possible. Through simulations and real-data applications, we evaluated the performance of these methodologies across various scenarios, including high-dimensional configurations.