We examine tests for jumps based on recent asymptotic results; we interpret the tests as Hausman-type tests. Monte Carlo evidence suggests that the daily ratio z-statistic has appropriate size, good power, and good jump detection capabilities revealed by the confusion matrix comprised of jump...

We examine the relationship between volatility and past and future returns using high-frequency aggregate equity index data. Consistent with a prolonged "leverage" effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to be...

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...