Generalized dynamic factor models and volatilities: recovering the market volatility shocks

Abstract

Decomposing volatilities into a common market-driven component and an idiosyncratic itemspecific one is an important issue in financial econometrics. This, however, requires the statistical analysis of large panels of time series, hence faces the usual challenges associated with highdimensional data. Factor model methods in such a context are an ideal tool, but they do not readily apply to the analysis of volatilities. Focusing on the reconstruction of the unobserved market shocks and the way they are loaded by the various items (stocks) in the panel, we propose an entirely non-parametric and model-free two-step general dynamic factor approach to the problem, which avoids the usual curse of dimensionality. Applied to the S&P100 asset return dataset, the method provides evidence that a non-negligible proportion of the market-driven volatility of returns originates in the volatilities of the idiosyncratic components of returns.JEL Classification: C32, C38, C58.

Generalized dynamic factor models and volatilities: estimation and forecasting

“…Assumptions (B1) and (B2) jointly imply that each of the two panels of log-volatility proxies admit a dynamic factor representation with q s and q w common shocks, respectively. Barigozzi and Hallin (2016) show that this is empirically justified for the financial data considered in this paper, with, moreover, q s = q w = 1.…”

“…In factor models for volatilities (approach (i)), common factors are interpreted as driving "market volatility" but nothing can be said about their relation to returns, as returns are not included in the analysis. On the other hand, in conditionally heteroskedastic factor models for returns (approach (ii)), volatility factors are typically identified as the conditional standard errors of the return-common factors-a gross oversimplification, as factor models for returns do not carry any information on a possible factor structure for volatilities (see Barigozzi and Hallin, 2016, for details and empirical confirmation).…”

“…Barigozzi and Hallin (2016) propose such an analysis, with a two-step dynamic factor approach of the problem based on the general or generalized dynamic factor model introduced in Forni et al (2000): a first dynamic factor model procedure, applied to the panel of returns, is extracting a (double) panel of volatility proxies which, in a second step, is analyzed via a second dynamic factor model procedure. Barigozzi and Hallin (2016), however, are focused on the objective of recovering volatility market shocks. Here, we go one step further, and show how the same two-step approach, possibly combined with an application of GARCH techniques, naturally produces forecasts of conditional volatilities.…”

“…This suggests, alongside the dynamic factor decomposition of returns, a dynamic factor decomposition of volatilities or volatility proxies. Based on this observation, Barigozzi and Hallin (2016) proposed an entirely non-parametric and model-free two-step general dynamic factor approach which accounts for a joint factor structure of returns and volatilities, and allows for extracting the market volatility shocks. Here, we go one step further, and show how the same two-step approach naturally produces volatility forecasts for the various stocks under study.…”

“…Merging those two sources of volatility is not good statistical practice, though, as the couples (e it , v it ) clearly carry more information than the sums (e it + v it ). As in Barigozzi and Hallin (2016), we therefore proceed with a joint volatility analysis of the two n × T panels at hand.…”