A useful application for copula functions is modeling the dynamics in the conditional moments of a time series. Using copulas, one can go beyond the traditional linear ARMA (p,q) modeling, which is solely based on the behavior of the autocorrelation function, and capture the entire dependence structure linking consecutive observations. This type of serial dependence is best represented by a canonical vine decomposition, and we illustrate this idea in the context of emerging stock markets, modeling linear and nonlinear temporal dependences of Brazilian series of realized volatilities. However, the analysis of intraday data collected from e-markets poses some specific challenges. The large amount of real-time information calls for heavy data manipulation, which may result in gross errors. Atypical points in high-frequency intraday transaction prices may contaminate the series of daily realized volatilities, thus affecting classical statistical inference and leading to poor predictions. Therefore, in this paper, we propose to robustly estimate pair-copula models using the weighted minimum distance and the weighted maximum likelihood estimates (WMLE). The excellent performance of these robust estimates for pair-copula models are assessed through a comprehensive set of simulations, from which the WMLE emerged as the best option for members of the elliptical copula family. We evaluate and compare alternative volatility forecasts and show that the robustly estimated canonical vine-based forecasts outperform the competitors. Copyright © 2013 John Wiley & Sons, Ltd.
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