A Model for Vast Panels of Volatilities
Universite Libre de Bruxelles - Solvay Brussels School of Economics and Management - ECARES
Universite Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES); National Fund for Scientific Research (FRS-FNRS)
March 28, 2012
Realized volatilities, when observed through time, share the following stylized facts: co--movements, clustering, long--memory, dynamic volatility, skewness and heavy--tails. We propose a dynamic factor model that captures these stylized facts and that can be applied to vast panels of volatilities as it does not suffer from the curse of dimensionality. It is an enhanced version of Bai and Ng (2004) in the following respects: i) we allow for long--memory in both the idiosyncratic and the common components, ii) the common shocks are conditionally heteroskedastic, and iii) the idiosyncratic and common shocks are skewed and heavy--tailed. Estimation of the factors, the idiosyncratic components and the parameters is simple: principal components and low dimension maximum likelihood estimations. A throughout Monte Carlo study shows the usefulness of the approach and an application to 90 daily realized volatilities, pertaining to S\&P100, from January 2001 to December 2008, evinces, among others, the following findings: i) All the volatilities have long--memory, more than half in the nonstationary range, that increases during financial turmoil. ii) Tests and criteria point towards one dynamic common factor driving the co--movements. iii) The factor has larger long--memory than the assets volatilities, suggesting that long--memory is a market characteristic. iv) The volatility of the realized volatility is not constant and common to all. v) A forecasting horse race against univariate short-- and long--memory models and short--memory dynamic factor models shows that our model outperforms short--, medium--, and long--run predictions, in particular in periods of stress.
Number of Pages in PDF File: 36
Keywords: Realized volatilities, vast dimensions, factor models, long-memory, forecasting
JEL Classification: C32, C51, G01working papers series
Date posted: September 14, 2011 ; Last revised: March 29, 2012
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