Enhancing Seasonal Adjustment Space Models: Constraints and Regularization for Improved Trend and AR Decomposition

TL;DR

This paper improves seasonal adjustment space models by introducing constraints and regularization techniques to better separate trend and AR components, addressing issues of over-smoothing and misattribution.

Contribution

It proposes novel constraints on AR eigenvalues and applies regularization methods to enhance model accuracy in seasonal adjustment within state space frameworks.

Findings

Constraints improve trend component estimation

Regularization reduces overfitting of AR models

Enhanced models outperform standard approaches on real data

Abstract

This paper investigates enhancements to model-based methods for seasonal adjustment, with a particular focus on the state space modeling framework. It addresses limitations of the standard Decomp model; specifically, the tendency to produce overly smooth trend components and the misattribution of long-term variation to the AR component when the eigenvalues of the AR model are close to unity. To mitigate these issues, the paper proposes imposing constraints on the modulus and argument of the AR eigenvalues, as well as applying regularization techniques ($L_1$ and $L_2$). These approaches are evaluated using real-world datasets. The paper is structured as follows: an overview of the Decomp model, a comparison with its noise-free variant, empirical assessment of constrained AR models, an exploration of regularization methods, and a concluding discussion of key insights.