Vector autoregression (VAR) of a moderate dimension and/or a long lag structure contains many parameters. A priori, many of these parameters are likely inconsequential and statistically insignificant if estimation is even feasible. Placing many zeros on a VAR either by theory and/or intuition has its limitations and practical difficulty. I provide a sequential Monte Carlo (SMC) combinatorial optimization algorithm to identify a stable parsimonious VAR as suggested by the data. This algorithm is a zero-norm approach by limiting the number of non-zero parameters, meaning that it finds the best-performing parsimonious VAR via a SMC optimization of a cross-validated likelihood function for the VAR while penalizes models with too many parameters. The resulting parsimonious model is stable and naturally interpretable. I demonstrate this algorithm on a VAR of seven macroeconomic variables studied in Smets and Wouters (2007, American Economic Review) and show how the resulting model characteristically differs from the typical Bayesian VAR.
Background reading: “Sequential Monte Carlo optimization and statistical inference” Duan, J.-C., Li, S., & Xu, Y. (2022). Wiley Integrative Reviews: Computational Statistics, e1598. https://doi.org/10.1002/wics.1598.