Estimation of Integrated Volatility

The financial econometrics literature mainly focuses on the integrated volatility and cross-volatility on a fixed time horizon. Therefore, this chapter is devoted to the estimation of these quantities. In the context of the Fourier estimation method, the integrated volatilities are computed by simply taking the 0-th Fourier coefficient in formula ( 2.13). We begin with the study of the univariate estimator, for the ease of notation; nevertheless, the results holding for this case can be easily extended to the multivariate estimator that will be studied in Section 3.3, with special care to be paid for the asynchronous data case. Then, the issue of feasibility for these results is discussed by providing an estimator of the error asymptotic variance, called quarticity. Finally, the properties of the Fourier estimator versus different integrated volatility estimators proposed in the literature are outlined.

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