Building on realized variance andbi-power variation measures constructed from high-frequencyfinancial prices, we propose a simple semiparametric framework foreffectively incorporating intraday data into modeling andforecasting of daily return volatility. We decompose the totaldaily return variability into the continuous sample path varianceand the discontinuous jumps over the trading day as well as theovernight return. Our empirical results, based on long samples ofhigh-frequency equity and bond futures returns, suggest that thedynamic dependencies in the daily continuous sample pathvariability is well described by an approximate long-memoryHAR-GARCH model, while the overnight returns may be captured by anaugmented GARCH type structure. Meanwhile, the non-parametricallyidentified jumps reveal interesting dynamic dependencies. We findthat combining an ACH model for the time-varying jump intensitywith a log-linear structure for the jump size does a good job indescribing the identified discontinuities. Lastly, we show how theresulting recursive three-component model structure may be used togenerate improved return volatility forecasts for the daily,weekly, and monthly horizons.
We examine tests for jumps based on recent asymptotic results; weinterpret the tests as Hausman-type tests. Monte Carlo evidencesuggests that the daily ratio $z$-statistic has appropriate size,good power, and good jump detection capabilities revealed by theconfusion matrix comprised of jump classification probabilities.We identify a pitfall in applying the asymptotic approximationover an entire sample. Theoretical and Monte Carlo analysisindicates that microstructure noise biases the tests againstdetecting jumps, and that a simple lagging strategy corrects thebias. Empirical work documents evidence for jumps that account forseven percent of stock market price variance.