Modelling High Dimension Distributions with High Frequency Data and Copulas

Résumé

This paper proposes a new general model for high dimension distributions of asset returns that utilizes high frequency data and copulas. The dependence between returns is decomposed into linear and nonlinear components, which enables the use of high frequency data to accurately measure and forecast linear dependence, and the use of a new class of copulas designed to capture nonlinear dependence between the resulting linearly uncorrelated residuals. Estimation of the new class of copulas is conducted using composite likelihood, making the model feasible even for hundreds of variables. A realistic simulation study verifies that multistage estimation with composite likelihood results in small loss in efficiency and large gain in computation speed. In- and out-of-sample tests confirm the statistical superiority of the proposed models applied to constituents of S&P100. To gauge economic significance, asset allocation decisions in an out-of-sample setting are compared.