Model reduction methods for vector autoregressive processes

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The study focuses on vector autoregressive (VAR) models, which have emerged as a key tool for analyzing macroeconomic time series over the past two decades. This modeling approach gained prominence following Sims' 1980 critique of traditional simultaneous equation models (SEM), which he argued relied on excessive restrictions based on presumed a priori knowledge. Sims championed largely unrestricted reduced form multivariate time series models, particularly VAR models, leading to their widespread use in examining the dynamics of time series systems. Over the years, various tools have been developed to analyze dynamic interactions among variables, including impulse response analysis and forecast error variance decompositions. The econometrics of VAR models is now well established and featured in numerous textbooks, such as those by Lütkepohl, Hamilton, Enders, Hendry, and Greene. The unrestricted VAR model offers a flexible framework that effectively summarizes economic time series data characteristics. However, this flexibility also introduces significant challenges, as each variable in an unrestricted VAR model is represented as a linear function of its own lagged values and those of all other variables in the system.