Time Series Analysis Based on Mixed-Effects Modeling and LSDV Estimation

Abstract

This paper proposes a modeling and analysis method based on a mixed-effects framework to address sudden performance improvements in complex systems. The core of this research lies in identifying and quantifying structural transitions embedded within time-series data through appropriate statistical and computational models. First, a breakpoint detection mechanism is designed to extract latent structural break signals from multidimensional time series, thereby filtering out sample sets exhibiting significant change characteristics. Second, at the model construction level, a mixed-effects modeling approach is introduced. This integrates key control factors and core state variables into a unified regression framework, while incorporating random disturbance terms to characterize heterogeneity differences, ensuring the model's interpretability and robustness. Finally, to address limitations in fixed-effects control, this study employs least squares dummy variable (LSDV) estimation. This technique transforms unobservable long-term differences into explicit dummy parameters for modeling, effectively mitigating omitted variable bias. The results demonstrate that this method can reliably identify and quantify structural transition effects across diverse scenarios, showcasing strong generalizability and practical applicability.