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 × 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.
Barigozzi M, Hallin M (2020). Generalized Dynamic Factor Models and Volatilities: Consistency, Rates, and Prediction Intervals. JOURNAL OF ECONOMETRICS, 216(1), 4-34 [10.1016/j.jeconom.2020.01.003].
Generalized Dynamic Factor Models and Volatilities: Consistency, Rates, and Prediction Intervals
Barigozzi M;
2020
Abstract
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 × 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.File | Dimensione | Formato | |
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BH_quantiles_final.pdf
Open Access dal 03/02/2022
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