Learning the Structure of a Nonstationary Vector Autoregression

Area of Science:

• Causal inference
• Time series analysis
• Econometrics

Background:

• Nonstationary time series data, particularly processes with stochastic trends, pose challenges for traditional causal discovery methods.
• Existing score-based causal discovery algorithms often struggle with integrated or cointegrated time series due to violations of statistical assumptions.

Purpose of the Study:

• To adapt existing graphical causal structure learning methods for application to nonstationary time series data exhibiting stochastic trends.
• To develop a modified scoring criterion that remains consistent for integrated or cointegrated processes.
• To enable the recovery of structural causal information from time series data, even in the presence of latent confounding factors.

Main Methods:

• Modification of the likelihood component within the Bayesian Information Criterion (BIC) score used in score-based causal discovery algorithms.
• Integration of the modified BIC score with the SVAR-GFCI (Structural Vector Autoregression - Generalized Functional Causality Inference) algorithm.
• Application and validation on both simulated datasets and real-world macroeconomic time series data.

Main Results:

• The modified BIC score ensures consistent model selection for integrated and cointegrated time series.
• The SVAR-GFCI algorithm, utilizing the enhanced score, successfully recovers qualitative structural information about the data-generating process.
• The approach demonstrates robustness in identifying causal structures despite the presence of unmeasured latent factors.

Conclusions:

• The proposed adaptation of causal structure learning methods provides a robust framework for analyzing nonstationary time series data.
• This methodology enhances the ability to uncover causal relationships in complex economic systems characterized by stochastic trends and potential latent confounders.
• The findings have significant implications for causal inference in econometrics and time series analysis.