Nonparametric Bayesian Volatility Learning Under Microstructure Noise

Gugushvili, Shota; Meulen, Frank van der; Schauer, Moritz; Spreij, Peter

doi:10.2139/ssrn.3178606

Cited by 5 publications

(3 citation statements)

References 31 publications

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“…Thereby our hope is that our work will contribute to further dissemination and popularisation of a nonparametric Bayesian approach to inference in SDEs, specifically with financial applications in mind. In that respect, see (Gugushvili et al, 2018may), that builds upon the present paper and deals with Bayesian volatility estimation under market microstructure noise. Our work can also be viewed as a partial fulfillment of anticipation in that some ideas developed originally in the context of audio and music processing "will also find use in other areas of science and engineering, such as financial or biomedical data analysis".…”

Section: Discussionmentioning

confidence: 95%

Nonparametric Bayesian Volatility Estimation

et al. 2018

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Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility with piecewise constant realisations on bins forming a partition of the time interval. The values on the bins are assigned an inverse Gamma Markov chain (IGMC) prior. Posterior inference is straightforward to implement via Gibbs sampling, as the full conditional distributions are available explicitly and turn out to be inverse Gamma. We also discuss in detail the hyperparameter selection for our method. Our nonparametric Bayesian approach leads to good practical results in representative simulation examples. Finally, we apply it on a classical data set in change-point analysis: weekly closings of the Dow-Jones industrial averages.

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Section: Discussionmentioning

confidence: 95%

Nonparametric Bayesian Volatility Estimation

et al. 2018

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“…The hyperparameter a controls the amount of smoothing in the gamma chain, with small values corresponding to less smoothing; we assume a ∼ Gamma(a a , b a ). For a statistical use of inverse gamma chains outside the sparsity context see, e.g., Gugushvili et al (2018a), Gugushvili et al (2019) and Gugushvili et al (2018b).…”

Section: Methodsmentioning

confidence: 99%

Bayesian wavelet de-noising with the caravan prior

et al. 2019

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According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising approach that takes into account such a feature of the signal may in practice outperform other, more vanilla methods, both in terms of the estimation error and visual appearance of the estimates. Motivated by this observation, we present a Bayesian approach to wavelet de-noising, where dependencies between neighbouring wavelet coefficients are a priori modelled via a Markov chain-based prior, that we term the caravan prior. Posterior computations in our method are performed via the Gibbs sampler. Using representative synthetic and real data examples, we conduct a detailed comparison of our approach with a benchmark empirical Bayes denoising method (due to Johnstone and Silverman). We show that the caravan prior fares well and is therefore a useful addition to the wavelet de-noising toolbox.

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“…The computer code to reproduce numerical examples in this article is available at Gugushvili et al (2022).…”

Section: Code Availabilitymentioning

confidence: 99%

Nonparametric Bayesian volatility learning under microstructure noise

Gugushvili

Meulen

Schauer

et al. 2022

Jpn J Stat Data Sci

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Nonparametric Bayesian Volatility Learning Under Microstructure Noise

Cited by 5 publications

References 31 publications

Nonparametric Bayesian Volatility Estimation

Nonparametric Bayesian Volatility Estimation

Bayesian wavelet de-noising with the caravan prior

Nonparametric Bayesian volatility learning under microstructure noise

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