A Dynamic Factor Model for Level and Volatility

2026-04-04

AI Summary

This study addresses the challenge of modeling state dependence and asymmetric tail risk in high-dimensional data by proposing an endogenous joint dynamic factor model. For the first time, it explicitly embeds the co-evolution of common level and volatility factors directly into the factor structure, thereby endogenously linking conditional means and variances within a large information set. The approach integrates latent dynamic factors, heavy-tailed heterogeneous shocks, second-moment co-movements in high-dimensional panels, and density forecasting techniques to effectively disentangle persistent uncertainty from transient outliers. Empirical results demonstrate that the model substantially improves predictive accuracy for tail distributions at medium-term horizons. Application to international inflation data reveals that advanced economies are predominantly driven by global level factors, whereas emerging economies exhibit stronger regional effects and greater contributions to volatility.

Abstract

This paper develops a dynamic factor model in which common level and volatility factors evolve jointly, allowing conditional means and variances to interact endogenously within a large-information setting. The joint evolution of these factors provides a tractable framework for modeling risk, as fluctuations in volatility affect both the dispersion and the location of outcomes, generating state-dependent and asymmetric tail risks in predictive distributions. Volatility is captured by latent common factors that drive co-movement in second moments across a large panel, while heavy-tailed idiosyncratic shocks absorb transitory outliers and isolate persistent uncertainty dynamics. The framework embeds these interactions directly within a factor structure, allowing risk to arise endogenously from the joint dynamics of the system rather than being imposed through reduced-form approaches. Empirically, the model delivers systematic improvements in density forecast accuracy, particularly in the tails of the predictive distribution and at medium horizons. An application to international inflation highlights a dominant global level component in advanced economies and stronger regional and volatility contributions in emerging and developing economies, pointing to substantial heterogeneity in the role of uncertainty across countries.

Problem

• dynamic factor model
• volatility
• level
• tail risk
• conditional variance

Innovation

• dynamic factor model
• joint level-volatility dynamics
• endogenous risk
• latent volatility factors
• density forecast