An Interpretable and Efficient Infinite-Order Vector Autoregressive Model for High-Dimensional Time Series

Abstract

As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long been hindered by its non-identifiability, computational intractability, and relative difficulty of interpretation. This paper introduces a novel infinite-order VAR model which, with only a little sacrifice of generality, inherits the essential temporal patterns of the VARMA model but avoids all of the above drawbacks. As another attractive feature, the temporal and cross-sectional dependence structures of this model can be interpreted separately, since they are characterized by different sets of parameters. For high-dimensional time series, this separation motivates us to impose sparsity on the parameters determining the cross-sectional dependence. As a result, greater statistical efficiency and interpretability can be achieved, while no loss of temporal information is incurred by the imposed sparsity. We introduce an ℓ 1 -regularized estimator for the proposed model and derive the corresponding nonasymptotic error bounds. An efficient block coordinate descent algorithm and a consistent model order selection method are developed. The merit of the proposed approach is supported by simulation studies and a real-world macroeconomic data analysis.

fnets: An R Package for Network Estimation and Forecasting via Factor-Adjusted VAR Modelling

“…We set (n, p) ∈ {(200, 10), (200,20), (500, 10), (500, 20)} where the range of p is in line with the simulation studies conducted in the relevant literature (see e.g. Zheng (2022)). We consider {1, 2, 3, 4} as the candidate VAR orders.…”

“…Step 2 and Step 3 of the network estimation methodology of FNETS involve the selection of the tuning parameters λ and η (see ( 11), ( 12) and ( 14)) and the VAR order d. While there exist a variety of methods available for VAR order selection in fixed dimensions (Lütkepohl, 2005, Chapter 4), the data-driven selection of d in high dimensions remains largely unaddressed with a few exceptions (Nicholson et al, 2020;Krampe and Margaritella, 2021;Zheng, 2022). We suggest two methods for jointly selecting λ and d for Step 2.…”