Sparse Identification and Estimation of Large-Scale Vector AutoRegressive Moving Averages.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Vector AutoRegressive Moving Average (VARMA) models are crucial for multivariate time series analysis.
• Identifiability challenges have historically limited VARMA model adoption in favor of simpler Vector AutoRegressive (VAR) models.
• Existing methods often struggle with the complexity and interpretability of VARMA models.

Purpose of the Study:

• To develop a novel optimization-based approach for VARMA model identification.
• To bridge the gap between theoretical VARMA models and practical time series analysis.
• To enhance the parsimony and efficiency of VARMA model estimation.

Main Methods:

• Utilized convex optimization to identify the most parsimonious parameterization among equivalent data-generating models.
• Employed a user-specified strongly convex penalty to quantify model simplicity.
• Developed an efficiently computable estimator based on the chosen penalty.

Main Results:

• Established consistency of the proposed estimators in a double-asymptotic regime.
• Provided non-asymptotic error bounds covering both model specification and parameter estimation.
• Demonstrated the method's advantage over traditional VAR approaches using three real-world datasets.

Conclusions:

• The proposed optimization-based method effectively addresses VARMA identifiability issues.
• This approach offers a more practical and parsimonious alternative to existing time series models.
• The findings have implications for large-scale time series algorithms and penalized regression analysis.