Sparse Tree-Based Aggregation for Time Series Regressions

2026-06-02

AI Summary

This study addresses the challenges of high-dimensional time series regression, particularly the curse of dimensionality and redundant lag terms that arise in high-order autoregressive and mixed-frequency settings. The authors propose StarTime, a novel method that introduces a tree-based hierarchical structure into lag modeling by organizing lagged variables according to their sampling frequencies. Coupled with convex regularization, this framework enables joint optimization of frequency-adaptive selection and sparsity. StarTime departs from conventional assumptions of fixed lag windows or uniform sparsity, offering a more flexible and theoretically grounded approach within the high-dimensional statistical estimation paradigm. Empirical results demonstrate substantial improvements in parameter estimation accuracy and structural recovery in simulations, and its effectiveness is further validated through applications to financial and macroeconomic datasets.

Abstract

High-dimensional time series regressions are often regularized to produce sparse coefficients. We show that temporal aggregation provides a powerful alternative to reduce dimensionality in high-order autoregressions and mixed-frequency regressions. To this end, we propose StarTime (Sparse Tree-based Aggregation for Time Series), a convex penalization method that uses a temporal tree to arrange lags hierarchically from high to low frequency. StarTime then flexibly selects coefficients to be aggregated at possibly varying frequencies, sparse or a combination thereof. We provide new error bounds for StarTime, demonstrate improved estimation accuracy and recovery of aggregation and sparsity in simulations relative to benchmarks, and illustrate StarTime's relevance for financial and macroeconomic applications.

Problem

• high-dimensional time series
• dimensionality reduction
• autoregression
• mixed-frequency regression
• sparsity

Innovation

• temporal aggregation
• hierarchical lag structure
• convex penalization
• high-dimensional time series
• mixed-frequency regression