Reinforcing the Moving Linear Model Approach: Theoretical Assessment of Parameter Estimation and Outlier Detection

This paper presents methodological advancements to enhance the moving linear (ML) model approach for time series analysis, with a particular focus on improving model eval- uation and outlier detection. The ML model decomposes time series data into constrained and remaining components, allowing for exible and effective analysis of economic uctua- tions. Building on this framework, the extended moving linear (EML) model introduces a mechanism for outlier detection by treating outliers as parameters estimated via maximum likelihood. However, challenges remain in providing theoretical support for parameter esti- mation and ensuring the stable identication of outlier locations. To address these issues, we rst develop a theoretically grounded evaluation criterion that enables coherent com- parison of model outcomes. Second, we propose a new outlier detection method based on maximizing the AIC reduction maximization method, offering a more systematic and effective approach. Empirical analyses using economic time series data demonstrate the improved performance and practical utility of the proposed enhancements.