Haar-Fisz Methodology for Interpretable Estimation of Large, Sparse, Time-Varying Volatility Matrices

• Activity Number: 636
• Type: Invited
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Piotr Fryzlewicz*+
• Companies: London School of Economics
• Keywords: Haar-Fisz ; volatility matrix ; non-stationarity ; high-dimensionality ; sparsity ; financial time series

Abstract

The emergence of the recent financial crisis, during which many markets underwent changes in their statistical structure over a short period of time, illustrates the importance of non-stationary modelling in financial time series. We start this talk by advocating a simple non-stationary multivariate model for financial returns. One task of critical importance to a financial analyst is accurate estimation of the volatility matrix, and in our model, this will be a time-varying quantity. Our estimation method is based on Haar wavelet thresholding, supplemented with the essential variance-stabilising Fisz transform (hence the name Haar-Fisz). Thanks to the use of Haar wavelets, our estimator: (a) has a natural in-built sparsity, i.e. local cross-market correlations are naturally estimated as zero wherever possible, which enhances the invertibility of the estimated matrix; (b) adequately captures sudden regime changes; (c) is theoretically tractable, also in the pointwise sense; (d) is rapidly computable, which is important if the matrix is large. We use real-data examples to illustrate our methodology.