Appendix to Realised Quantile-Based Estimation of the Integrated Variance

2009 ◽  
Author(s):  
Kim Christensen ◽  
Roel C. A. Oomen ◽  
Mark Podolskij
Keyword(s):  
Integrated Variance

scholarly journals Time-bridge estimators of integrated variance

2013 ◽  
Vol 2 (2) ◽  
pp. 71-108 ◽  
Author(s):  
Alexander Saichev ◽  
Didier Sornette
Keyword(s):  
Integrated Variance

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

2019 ◽  
Author(s):  
Giuseppe Buccheri ◽  
Fulvio Corsi
Keyword(s):  
Long Memory ◽  
Measurement Errors ◽  
Asymptotic Theory ◽  
Linear Models ◽  
Real Data ◽  
Realized Variance ◽  
Likelihood Methods ◽  
Out Of Sample ◽  
Maximum Likelihood Methods ◽  
Integrated Variance

Abstract 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.

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

2016 ◽  
Vol 33 (6) ◽  
pp. 1457-1501 ◽  
Author(s):  
Rasmus Tangsgaard Varneskov
Keyword(s):  
Rate Of Convergence ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Bias Reduction ◽  
Quadratic Variation ◽  
Optimal Rate ◽  
Good Efficiency ◽  
Optimal Rate Of Convergence ◽  
Integrated Variance ◽  
Exogenous Noise

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.

Integrated Variance Reduction Strategies for Simulation

1996 ◽  
Vol 44 (2) ◽  
pp. 327-346 ◽  
Author(s):  
Athanassios N. Avramidis ◽  
James R. Wilson
Keyword(s):  
Variance Reduction ◽  
Reduction Strategies ◽  
Integrated Variance
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