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On the Interaction between Ultra–high Frequency Measures of Volatility

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Abstract

We analyze several measures of volatility (realized variance, bipower variation and squared daily returns) as estimators of integrated variance of a continuous time stochastic process for an asset price. We use a Multiplicative Error Model to describe the evolution of each measure as the product of its conditional expectation and a positive valued iid innovation. By inserting past values of each measure and asymmetric effects based on the sign of the return in the specification of the conditional expectation, one can investigate the information content of each indicator relative to the others. The results show that there is a directed dynamic relationship among measures, with squared returns and bipower variance interdependent with one another, and affecting realized variance without any feed-back from the latter.

Suggested Citation

  • Giampiero Gallo & Margherita Velucchi, 2007. "On the Interaction between Ultra–high Frequency Measures of Volatility," Econometrics Working Papers Archive wp2007_01, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    • Handle: RePEc:fir:econom:wp2007_01
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    Keywords

    Volatility; Multiplicative Error Models; Realized Variance; Bi-power Variance; Squared Returns; Jumps.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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