Harrison Katz, Robert E. Weiss
arXiv 7 Apr 2025 · Statistics — Methodology
arXiv:2504.05489 · PDF · Extracted main text
High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare three Bayesian shrinkage priors (horseshoe, lasso, and normal) and two frequentist regularization approaches (ridge and nonparametric shrinkage) under three carefully crafted simulation scenarios. These scenarios encompass (i) overfitting in a low-dimensional setting, (ii) sparse high-dimensional processes, and (iii) a combined scenario where both large dimension and overfitting complicate inference. We evaluate each method in quality of parameter estimation (root mean squared error, coverage, and interval length) and out-of-sample forecasting (one-step-ahead forecast RMSE). Our findings show that local-global Bayesian methods, particularly the horseshoe, dominate in maintaining accurate coverage and minimizing parameter error, even when the model is heavily over-parameterized. Frequentist ridge often yields competitive point forecasts but underestimates uncertainty, leading to sub-nominal coverage. A real-data application using macroeconomic variables from Canada illustrates how these methods perform in practice, reinforcing the advantages of local-global priors in stabilizing inference when dimension or lag order is inflated.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Carvalho, Carlos M and Polson, Nicholas G and Scott, James G (2010) The Horseshoe Estimator for Sparse Signals | 0.644 | 2 | 2 | 100% |
| 2 | Trevor Park and George Casella (2008) The Bayesian Lasso | 0.644 | 2 | 2 | 100% |
| 3 | Makalic, Enes and Schmidt, Daniel F (2016) A Simple Sampler for the Horseshoe Estimator | 0.644 | 2 | 2 | 100% |
| 4 | Huber, Florian and Koop, Gary (2023) Subspace Shrinkage in Conjugate Bayesian Vector Autoregressions | 0.511 | 2 | 1 | 100% |
| 5 | Zhou, Xiaodan and Chan, Joshua CC (2023) Factor-augmented high-dimensional VARs with structured priors: New perspectives for macroeconomic forecasting | 0.511 | 2 | 1 | 100% |
| 6 | Stock, James H and Watson, Mark W (2002) Macroeconomic Forecasting Using Diffusion Indexes | 0.511 | 2 | 1 | 100% |
| 7 | Aprigliano, Valentina (2020) A large Bayesian VAR with a block-specific shrinkage: A forecasting application for Italian industrial production | 0.405 | 1 | 1 | 100% |
| 8 | Bańbura, Marta and Giannone, Domenico and Lenza, Michele (2010) Large Bayesian vector auto regressions | 0.405 | 1 | 1 | 100% |
| 9 | Barigozzi, Matteo and Cho, Haeran and Owens, Dom (2024) FNETS: Factor-Adjusted Network Estimation and Forecasting for High-Dimensional Time Series | 0.405 | 1 | 1 | 100% |
| 10 | Basu, Sumanta and Shojaie, Ali and Michailidis, George (2019) Low Dimensional Representations for High Dimensional Vector Autoregressions with Structured Penalties | 0.405 | 1 | 1 | 100% |
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