Frequency Domain Estimation of Integrated Volatility for Itô Processes in the Presence of Market-Microstructure Noise

Olhede, Sofia C.; Sykulski, Adam M.; Pavliotis, Grigorios A.

doi:10.1137/090756363

Cited by 21 publications

(14 citation statements)

References 39 publications

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“…A common approach towards addressing this problem is to subsample the data, see [1,5,6,51,52,61,63,64,83,88] for methodological aspects. For specific applications see [78] (multiscale inverse problems), [2,82,105] (economics and finance), and [28,103] (ocean and atmospheric science).…”

Section: Parameter Estimation and Filtering In Multiscale Systemsmentioning

confidence: 99%

“…Clearly, the RP-EnKF deals adequately with multiscale data, while the EnKF fails to recover the true parameter θtrue in this setting. We would like to stress that the RP-EnKF scheme has been implemented without area correction, that is imposing Y k = Y sym k as defined in (82). The choice Y skew k = 0 is motivated by a plot analogous and qualitatively similar to Figure 4c (omitted due to space considerations), showing that subsampling does not indicate substantial Lévy area terms (intuitively, the dynamics (100) does not contain significant 'rotational' contributions in the regime ε → 0).…”

Section: Homogenisation In a Two-scale Potentialmentioning

confidence: 99%

“…Naturally, real-world data is almost always complex, multiscale, and increasingly high-dimensional, whereas the corresponding mathematical abstractions are often preferred to be simple and of comparatively low resolution. The discrepancy between intricate data and reducedorder models poses a significant challenge for their simultaneous treatment, and the failure of some standard statistical approaches in scenarios of this type is well documented [2,82,89,103,105].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering

Coghi¹,

Nilssen²,

Nüsken³

et al. 2021

Preprint

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Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting particle system, which in turn is suggestive of a numerical scheme that can be viewed as an extension of the ensemble Kalman filter to a rough-path framework. Finally, we discuss a data-driven method based on subsampling to construct suitable rough path lifts and demonstrate the robustness of our scheme in a number of numerical experiments related to parameter estimation problems in multiscale contexts.

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Section: Parameter Estimation and Filtering In Multiscale Systemsmentioning

confidence: 99%

Section: Homogenisation In a Two-scale Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering

Coghi¹,

Nilssen²,

Nüsken³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Similar techniques can be employed in econometrics, in particular for the estimation of the integrated stochastic volatility in the presence of market microstructure noise. In this case, too, the data have to be subsampled at an appropriate rate [6,25]. The correct subsampling rate can, in some instances, be rather extreme with respect to the frequency of the data itself, resulting in ignoring as much as 99% of the time series.…”

Section: Literature Reviewmentioning

confidence: 99%

Drift Estimation of Multiscale Diffusions Based on Filtered Data

et al. 2021

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We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift coefficient of the homogenized equation requires pre-processing of the data, often in the form of subsampling; this is because the two-scale equation and the homogenized single-scale equation are incompatible at small scales, generating mutually singular measures on the path space. We avoid subsampling and work instead with filtered data, found by application of an appropriate kernel function, and compute maximum likelihood estimators based on the filtered process. We show that the estimators we propose are asymptotically unbiased and demonstrate numerically the advantages of our method with respect to subsampling. Finally, we show how our filtered data methodology can be combined with Bayesian techniques and provide a full uncertainty quantification of the inference procedure.

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“…Authors utilize wavelets to build the methodology for the estimation of jumps. Finally, Mancino and Sanfelici (2008), Olhede et al (2009) propose estimators based on the Fourier transform. While the idea is very similar, this approach leads to realized volatility measurement in the frequency domain solely.…”

mentioning

confidence: 99%

Realized wavelet-based estimation of integrated variance and jumps in the presence of noise

Baruník

Vácha

2015

Quantitative Finance

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We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator in the two-scale realized variance framework, we are able to utilize all available data and get feasible estimator in the presence of microstructure noise as well. The estimator is tested in a large numerical study of the finite sample performance and is compared to other popular realized variation estimators. We use different simulation settings with changing noise as well as jump level in different price processes including long memory fractional stochastic volatility model. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Our time-frequency estimators not only produce feasible estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with better understanding of the volatility dynamics.

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Frequency Domain Estimation of Integrated Volatility for Itô Processes in the Presence of Market-Microstructure Noise

Cited by 21 publications

References 39 publications

Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering

Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering

Drift Estimation of Multiscale Diffusions Based on Filtered Data

Realized wavelet-based estimation of integrated variance and jumps in the presence of noise

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