HARK the SHARK: Realized Volatility Modeling with Measurement Errors and Nonlinear Dependencies*

Despite their effectiveness, linear models for realized variance neglect measurement errors on integrated variance and exhibit several forms of misspecification due to the inherent nonlinear dynamics of volatility. We propose new extensions of the popular approximate long-memory heterogeneous autoregressive (HAR) model apt to disentangle these effects and quantify their separate impact on volatility forecasts. By combining the asymptotic theory of the realized variance estimator with the Kalman filter and by introducing time-varying HAR parameters, we build new models that account for: (i) measurement errors (HARK), (ii) nonlinear dependencies (SHAR) and (iii) both measurement errors and nonlinearities (SHARK). The proposed models are simply estimated through standard maximum likelihood methods and are shown, both on simulated and real data, to provide better out-of-sample forecasts compared to standard HAR specifications and other competing approaches.

ESTIMATING THE QUADRATIC VARIATION SPECTRUM OF NOISY ASSET PRICES USING GENERALIZED FLAT-TOP REALIZED KERNELS

This paper analyzes a generalized class of flat-top realized kernel estimators for the quadratic variation spectrum, that is, the decomposition of quadratic variation into integrated variance and jump variation. The underlying log-price process is contaminated by additive noise, which consists of two orthogonal components to accommodate α-mixing dependent exogenous noise and an asymptotically non-degenerate endogenous correlation structure. In the absence of jumps, the class of estimators is shown to be consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, n1/4. Exact bounds on lower-order terms are obtained, and these are used to propose a selection rule for the flat-top shrinkage. Bounds on the optimal bandwidth for noise models of varying complexity are also provided. In theoretical and numerical comparisons with alternative estimators, including the realized kernel, the two-scale realized kernel, and a bias-corrected pre-averaging estimator, the flat-top realized kernel enjoys a higher-order advantage in terms of bias reduction, in addition to good efficiency properties. The analysis is extended to jump-diffusions where the asymptotic properties of a flat-top realized kernel estimate of the total quadratic variation are established. Apart from a larger asymptotic variance, they are similar to the no-jump case. Finally, the estimators are used to design two classes of (medium) blocked realized kernels, which produce consistent, non-negative estimates of integrated variance. The blocked estimators are shown to have no loss either of asymptotic efficiency or in the rate of consistency relative to the flat-top realized kernels when jumps are absent. However, only the medium blocked realized kernels achieve the optimal rate of convergence under the jump alternative.

Real-time QRS detection using integrated variance for ECG gated cardiac MRI

During magnetic resonance imaging (MRI), a patient’s vital signs are required for different purposes. In cardiac MRI (CMR), an electrocardiogram (ECG) of the patient is required for triggering the image acquisition process. However, a reliable QRS detection of an ECG signal acquired inside an MRI scanner is a challenging task due to the magnetohydrodynamic (MHD) effect which interferes with the ECG. The aim of this work was to develop a reliable QRS detector usable inside the MRI which also fulfills the standards for medical devices (IEC 60601-2-27). Therefore, a novel real-time QRS detector based on integrated variance measurements is presented. The algorithm was trained on ANSI/AAMI EC13 test waveforms and was then applied to two databases with 12-lead ECG signals recorded inside and outside an MRI scanner. Reliable results for both databases were achieved for the ECG signals recorded inside (DBMRI: sensitivity Se = 99.94%, positive predictive value +P = 99.84%) and outside (DBInCarT: Se = 99.29%, +P = 99.72%) the MRI. Due to the accurate R-peak detection in real-time this can be used for monitoring and triggering in MRI exams.