Our objective is volatility forecasting, which is core to many risk management problems. We provide theoretical explanations for (i) the empirical stylized fact recognized at least since Taylor (1986) and Ding, Granger, and Engle (1993) that absolute returns show more persistence than squared...

We analyze the effects of nonsynchronicity and market microstructure noise on realized covariance type estimators. Hayashi and Yoshida (2005) propose a simple estimator that resolves the problem of nonsynchronicity and is unbiased and consistent for the integrated covariance in the absence of...

We derive necessary and sufficient conditions for the positive definiteness of the predicted volatility matrix in a bivariate autoregressive volatility specification. These nonlinear inequality restrictions have strong implications in terms of causality between volatilities and covolatilities....