Empirical validation of novel non-asymptotic bounds on the least squares estimator for LTI systems with applications in economics

This study aims to investigate the performance of new theoretical non-asymptotic bounds of the least squares estimator for linear time-invariant (LTI) state-space models, building on prior foundational research.Using both simulated and real-world datasets, the analysis examines the influence of noise characteristics, controllability and noise conditioning on estimation accuracy. Furthermore, the study validates the derived bounds on real datasets through, among others, cross-validation and bootstrap techniques.The results confirm the validity of the theoretical non-asymptotic error bounds across various system configurations. Key insights highlight the role of system stability, dimensionality and noise properties in shaping estimation performance.While this study focuses on specific configurations and datasets, expanding the scope to include alternative estimation techniques and broader real-world systems could yield additional insights into the practical applicability of these bounds.The findings provide actionable insights and practical guidelines for improving econometric modeling, financial time-series forecasting, adaptive systems control and environmental modeling, enabling improved system identification and parameter estimation techniques in these domains.By using real datasets and advanced validation techniques, this study bridges the gap between theoretical bounds and practical applications, hopefully opening a novel perspective on least squares estimation performance in LTI systems.