Volatilities, in high-dimensional panels of economic time series with a dynamic factor structure on the levels or returns, typically also admit a dynamic factor decomposition. A two-stage dynamic factor model method recovering  common and idiosyncratic volatility shocks therefore was proposed in Barigozzi and Hallin (2016). By exploiting this two-stage factor approach, we build one-step-ahead conditional prediction intervals for large n \times T panels of returns. We provide consistency and consistency rates results for the proposed estimators as both n and T tend to infinity.  Finally, we apply our methodology to a panel of asset returns belonging to the S&P100 index in order to compute one-step-ahead conditional prediction intervals for the period 2006-2013. A comparison with the componentwise GARCH (1,1) benchmark (which does not take advantage of cross-sectional information) demonstrates the superiority of our approach, which is genuinely multivariate (and high-dimensional), nonparametric, and model-free.
Volatilities, in high-dimensional panels of economic time series with a dynamic factor structure on the levels or returns, typically also admit a dynamic factor decomposition. We consider a two-stage dynamic factor model method recovering the common and idiosyncratic components of both levels and log-volatilities. Specifically, in a first estimation step, we extract the common and idiosyncratic shocks for the levels, from which a log-volatility proxy is computed. In a second step, we estimate a dynamic factor model, which is equivalent to a multiplicative factor structure for volatilities, for the log-volatility panel. By exploiting this two-stage factor approach, we build one-step-ahead conditional prediction intervals for large n \times T panels of returns. Those intervals are based on empirical quantiles, not on conditional variances; they can be either equal- or unequal- tailed. We provide uniform consistency and consistency rates results for the proposed estimators as both n and T tend to infinity. We study the finite-sample properties of our estimators by means of Monte Carlo simulations. Finally, we apply our methodology to a panel of asset returns belonging to the S&P100 index in order to compute one-step-ahead conditional prediction intervals for the period 2006-2013. A comparison with the componentwise GARCH benchmark (which does not take advantage of cross-sectional information) demonstrates the superiority of our approach, which is genuinely multivariate (and high-dimensional), nonparametric, and model-free.
R
A
We consider a
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the
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volatility shocks therefore was proposed in Barigozzi and Hallin (2016).
components of both levels and log-volatilities. Specifically, in a first estimation step, we extract the common and idiosyncratic shocks for the levels, from which a log-volatility proxy is computed. In a second step, we estimate a dynamic factor model, which is equivalent to a multiplicative factor structure for volatilities, for the log-volatility panel.
R
We provide
Those intervals are based on empirical quantiles, not on conditional variances; they can be either equal- or unequal- tailed. We provide uniform
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We study the finite-sample properties of our estimators by means of Monte Carlo simulations.
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(1,1)