Title: Robust sufficient dimension reduction for multivariate time series analysis Authors:  Amal Alqarni - Cardiff University (United Kingdom) [presenting]
Abstract: Sufficient dimension reduction (SDR) is a statistical framework that is widely used to reduce high-dimensional data while maintaining significant information. It has applications in a wide range of domains. The previous methodology of SDR in the context of multivariate time series analysis (like TSIR) is extended, addressing complex challenges such as high dimensionality, temporal relationships, and noise arising from heavy-tailed outliers. We propose a novel methodology for robust dimension reduction in multivariate time series analysis: Time-series Sliced Inverse Median Difference (TSIMeD). TSIMeD achieves robust dimension reduction by identifying key temporal directions and lags, even in the presence of heavy-tailed outliers. To enhance dimension selection, we propose a Bayesian Information Criterion (BIC)-type method, improving model interpretability and efficiency. Extensive simulations demonstrate that TSIMeD outperforms established methods like Time Series Sliced Inverse Regression (TSIR) and Sliced Inverse Mean Difference (TSIMD), requiring fewer directions while maintaining superior accuracy across a variety of lag settings and noise conditions, highlighting their transformative potential for multivariate time series analysis.