Over the Stability Space of a Multivariate Time Series

TL;DR

This paper introduces the concept of stability space for multivariate time series to better capture stationary components amid non-stationarity and high dimensionality, proposing non-parametric estimation methods and evaluating their performance.

Contribution

It presents a novel stability space framework and two non-parametric procedures for estimating it, extending classical cointegration analysis to high-dimensional, non-stationary contexts.

Findings

The proposed methods effectively identify stationary components in high-dimensional data.

Simulation results show competitive performance compared to traditional parametric methods.

Application to real data demonstrates practical utility in complex scenarios.

Abstract

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 prioritise 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 where regularisation techniques are explored, considering a sparse version of the Principal Component Analysis.