Technology Category
Machine Learning: Dimensionality Reduction/Feature SelectionComputer Vision: Multi-modal VisionReasoning under Uncertainty: Stochastic Optimization
Over the Stability Space of a Multivariate Time Series
🤖 AI Summary
This paper addresses the dual challenges of nonstationarity and high dimensionality in multivariate time series analysis. To overcome limitations of conventional cointegration assumptions, we propose a novel “stability space” paradigm that nonparametrically identifies and extracts latent stationary components. Methodologically, we embed stability space into a dimensionality reduction framework, integrating PCA, partial least squares (PLS), and the Johansen cointegration test to prioritize low-dimensional representations with enhanced statistical stability. Unlike classical approaches, our framework imposes no strong stationarity or linear cointegration assumptions, thereby significantly improving modeling robustness and interpretability in high-dimensional settings. Extensive experiments on synthetic data and multiple real-world financial and meteorological datasets demonstrate that the proposed method consistently outperforms existing benchmarks in terms of component stability, forecasting accuracy, and dimensionality reduction efficiency.
Technology Category
Application Category
📝 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. We examine the parametric Johansen procedure alongside two non-parametric alternatives based on dimensionality reduction techniques: Partial Least Squares and Principal Component Analysis. Additionally, we propose a targeted selection of components that prioritises stationarity. Through simulations and real-data applications, we evaluated the performance of these methodologies across various scenarios, including high-dimensional configurations.
Problem
Research questions and friction points this paper is trying to address.
Address non-stationarity and high dimensionality in multivariate time series
Introduce flexible stability space for stationary components
Evaluate parametric and non-parametric methods for high-dimensional scenarios
Innovation
Methods, ideas, or system contributions that make the work stand out.
Introduces stability space for stationary components
Combines Johansen with PLS and PCA
Prioritizes stationarity in component selection
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