🤖 AI Summary
This study addresses the challenge of effectively integrating structural information from multiple channels in large-scale dynamic systems. To this end, the authors propose a time-varying multilayer network vector autoregressive (TV-MLN-VAR) model combined with a penalized model averaging approach that dynamically combines multiple candidate models to capture cross-channel spillover effects. The work innovatively introduces time-varying optimal model averaging weights and, for the first time, extends conformal prediction to locally stationary time series to construct valid prediction intervals. Theoretical analysis establishes the asymptotic optimality and convergence rate of the weight estimator. Extensive simulations and empirical applications to CPI inflation forecasting demonstrate that the proposed method achieves strong estimation and predictive performance even in finite samples.
📝 Abstract
In this paper, we introduce a flexible time-varying multi-layer network vector autoregression (VAR) model framework for large-scale time series, allowing agents in dynamic systems to interact through multiple channels and incorporating multiple adjacency matrices to capture network spillover effects. We propose a penalized model averaging method to determine a time-varying optimal combination of multi-layer network VAR candidate models whose number may be divergent. Under some regularity conditions, the asymptotic properties such as asymptotic optimality and convergence rates of the proposed time-varying weight estimation are derived in the contexts of both the in-sample fitting and out-of-sample prediction. In addition, we extend the conformal prediction method to construct prediction bands for locally stationary time series. Monte-Carlo simulation studies and an empirical application to forecast CPI inflation by combining multiple network information are given to illustrate reliable finite-sample estimation and predictive performance of the developed methodology.