Identification Verification for Structural Vector Autoregressions with Sparse Heterogeneous Markov Switching Heteroskedasticity

2026-03-16

AI Summary

This study addresses the identification uncertainty in structural vector autoregressive (SVAR) models arising from heteroskedasticity under time-varying volatility. To this end, the authors propose a sparse heterogeneous Markov-switching heteroskedastic SVAR model, wherein the conditional variances of individual structural shocks are governed by independent Markov processes. The model incorporates a sparsity mechanism to eliminate inactive states and introduces a normalized conditional variance distribution to facilitate Gibbs sampling and identification validation. By innovatively integrating Bayesian inference, sparse state representation, and structural normalization, the approach not only enables reliable testing of the homoskedasticity assumption but also substantially improves the accuracy and reliability of structural parameter estimation. Empirical results demonstrate that the model effectively identifies U.S. monetary policy shocks in macro-financial data and achieves predictive performance comparable to stochastic volatility models.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Structured Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We propose a structural vector autoregressive model with a new and flexible specification of the volatility process which we call Sparse Heterogeneous Markov-Switching Heteroskedasticity. In this model, the conditional variance of each structural shock changes in time according to its own Markov process. Additionally, it features a sparse representation of Markov processes, in which the number of regimes is set to exceed that of the data-generating process, with some regimes allowed to have zero occurrences throughout the sample. We complement these developments with a definition of a new distribution for normalised conditional variances that facilitates Gibbs sampling and identification verification. In effect, our model: (i) normalises the system and estimates the structural parameters more precisely than popular alternatives; (ii) can be used to verify homoskedasticity reliably and, thus, inform identification through heteroskedasticity; and (iii) features excellent forecasting performance comparable with Stochastic Volatility. Finally, revisiting a prominent macro-financial structural system, we provide evidence for the identification of the US monetary policy shock via heteroskedasticity, with estimates consistent with those reported in the literature.

Problem

• Structural Vector Autoregression
• Identification Verification
• Markov-Switching Heteroskedasticity
• Sparse Heterogeneous Volatility
• Heteroskedasticity-based Identification

Innovation

• Sparse Heterogeneous Markov-Switching
• Structural Vector Autoregression
• Heteroskedasticity-based Identification
• Gibbs Sampling
• Conditional Variance Normalization