Principal Volatility Component Analysis

• Activity Number: 276
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: JBES-Journal of Business & Economic Statistics
• Author(s): Ruey S. Tsay*+ and Yu-Pin Hu
• Companies: The University of Chicago and National Chi Nan University
• Keywords: Common volatility component ; Conditional heteroscedasticity ; Foreign exchange rate ; Generalized covariance matrix ; Generalized kurtosis matrix ; Principal component analysis

Abstract

Many empirical time series such as asset returns and traffic data exhibit the characteristic of time-varying conditional covariance, known as volatility or conditional heteroscedasticity. Modeling multivariate volatility, however, encounters several difficulties, including the curse of dimensionality. Dimension reduction can be useful and is often necessary. The goal of this paper is to extend the idea of principal component analysis to principal volatility component (PVC) analysis. We define a cumulative generalized kurtosis matrix to summarize the volatility dependence of multivariate time series. Spectral decomposition of this generalized kurtosis matrix is used to define principal volatility components. We consider a sample estimate of the generalized kurtosis matrix and propose test statistics for detecting linear combinations that do not have conditional heteroscedasticity. For application, we applied the proposed analysis to weekly log returns of 7 exchange rates against U.S. dollar from 2000 to 2011 and found a linear combination among the exchange rates that have no conditional heteroscedasticity.