Nonparametric Bayesian Volatility Estimation
| Autor: | Gugushvili, S., van der Meulen, F., Schauer, M., Spreij, P., Wood, D.R., de Gier, J., Praeger, C.E., Tao, T. |
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| Přispěvatelé: | Stochastics (KDV, FNWI) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Hyperparameter
Markov chain 05 social sciences Conditional probability distribution 01 natural sciences 010104 statistics & probability symbols.namesake Stochastic differential equation Discrete time and continuous time 0502 economics and business symbols Piecewise Applied mathematics 0101 mathematics Volatility (finance) 050205 econometrics Gibbs sampling Mathematics |
| Zdroj: | 2017 MATRIX Annals ISBN: 9783030041601 2017 MATRIX Annals, 279-302 STARTPAGE=279;ENDPAGE=302;TITLE=2017 MATRIX Annals |
| ISSN: | 2523-3041 |
| DOI: | 10.1007/978-3-030-04161-8_19 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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