Informing VAR(1) with qualitative dynamical features improves predictive accuracy.

Area of Science:

• Psychological time series analysis
• Dynamical systems modeling
• Statistical modeling

Background:

• Autoregressive (AR) models often outperform general Vector Autoregression (VAR) models for affective time series.
• Existing VAR models with lasso penalties (VAR-lasso) remain too complex, hindering the selection of simpler, more interpretable models.

Purpose of the Study:

• To propose a novel reparametrization of VAR models using a symmetric and antisymmetric decomposition (SAD).
• To introduce a new regularization technique, SAD-lasso, for improved model selection and interpretation in time series analysis.
• To compare the predictive accuracy of SAD-lasso against VAR-lasso using psychological time series data.

Main Methods:

• Reparametrization of the VAR model transition matrix into symmetric and antisymmetric components.
• Application of the lasso penalty to the decomposed components (SAD-lasso).
• Analysis of 1,391 psychological time series of affect to evaluate predictive accuracy.

Main Results:

• SAD-lasso demonstrates superior regularization performance compared to VAR-lasso.
• The SAD decomposition allows for targeted selection of distinct dynamical features like relaxation, shearing, and oscillations.
• Symmetric VAR models, a subclass derived from SAD, extend AR models by allowing component interactions.

Conclusions:

• SAD-lasso provides a more effective and interpretable approach to modeling affective time series than VAR-lasso.
• The study suggests the prevalence of symmetric interactions in nearly half of the analyzed psychological time series.
• The proposed method enhances the ability to uncover complex dynamics in psychological data.