Cholesky Factorization Method for VARMA Modeling of Residual Volatilities of Single- and Mixed-Frequency Data

• Activity Number: 385
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Peter Zadrozny and Klaus Wohlrabe*+ and Stefan Mittnik
• Companies: Bureau of Labor Statistics and Ifo Institut and Ludwig-Maxilians-Universität München
• Keywords: multiple time-series modelling ; dynamic factor modelling ; Tikhonov regularization ; missing data

Abstract

The paper describes and applies a Cholesky factorization method for jointly VARMA modelling the residual volatilities of multiple, single- or mixed-frequency, time-series data. The key step in the method is adding the same, small, scalar matrix to the outer-product matrix of residuals in each period in order to make it nonsingular and, thus, Cholesky factorizable. This step is analogous to adding a scalar matrix to the design matrix in OLS regression and making it a ridge regression. The method has a main advantage of allowing prior data analysis before estimating a model, which in practice avoids estimating many inadequately specified models. By contrast, common VEC and BEKK methods don't admit prior data analysis and require nonlinear estimation of parameters whose number rises quagdratically with the number of series. Although the realized daily volatility modelling method also allows prior data analysis, unlike the present method, it requires that there be fewer series than intraday sample periods.