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Partially censored posterior for robust and efficient risk evaluation

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Partially censored posterior for robust and efficient risk evaluation. / Borowska, Agnieszka; Hoogerheide, Lennart; Koopman, Siem Jan; van Dijk, Herman K.

In: Journal of Econometrics, Vol. 217, No. 2, 2020, p. 335-355.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articlepeer-review

Harvard

Borowska, A, Hoogerheide, L, Koopman, SJ & van Dijk, HK 2020, 'Partially censored posterior for robust and efficient risk evaluation', Journal of Econometrics, vol. 217, no. 2, pp. 335-355. https://doi.org/10.1016/j.jeconom.2019.12.007

APA

Borowska, A., Hoogerheide, L., Koopman, S. J., & van Dijk, H. K. (2020). Partially censored posterior for robust and efficient risk evaluation. Journal of Econometrics, 217(2), 335-355. https://doi.org/10.1016/j.jeconom.2019.12.007

CBE

Borowska A, Hoogerheide L, Koopman SJ, van Dijk HK. 2020. Partially censored posterior for robust and efficient risk evaluation. Journal of Econometrics. 217(2):335-355. https://doi.org/10.1016/j.jeconom.2019.12.007

MLA

Vancouver

Borowska A, Hoogerheide L, Koopman SJ, van Dijk HK. Partially censored posterior for robust and efficient risk evaluation. Journal of Econometrics. 2020;217(2):335-355. https://doi.org/10.1016/j.jeconom.2019.12.007

Author

Borowska, Agnieszka ; Hoogerheide, Lennart ; Koopman, Siem Jan ; van Dijk, Herman K. / Partially censored posterior for robust and efficient risk evaluation. In: Journal of Econometrics. 2020 ; Vol. 217, No. 2. pp. 335-355.

Bibtex

@article{05f708cca4a0456fa570175da6cc3790,
title = "Partially censored posterior for robust and efficient risk evaluation",
abstract = "A novel approach to inference for a specific region of the predictive distribution is introduced. An important domain of application is accurate prediction of financial risk measures, where the area of interest is the left tail of the predictive density of logreturns. Our proposed approach originates from the Bayesian approach to parameter estimation and time series forecasting, however it is robust in the sense that it provides a more accurate estimation of the predictive density in the region of interest in case of misspecification. The first main contribution of the paper is the novel concept of the Partially Censored Posterior (PCP), where the set of model parameters is partitioned into two subsets: for the first subset of parameters we consider the standard marginal posterior, for the second subset of parameters (that are particularly related to the region of interest) we consider the conditional censored posterior. The censoring means that observations outside the region of interest are censored: for those observations only the probability of being outside the region of interest matters. This quasi-Bayesian approach yields more precise parameter estimation than a fully censored posterior for all parameters, and has more focus on the region of interest than a standard Bayesian approach. The second main contribution is that we introduce two novel methods for computationally efficient simulation: Conditional MitISEM, a Markov chain Monte Carlo method to simulate model parameters from the Partially Censored Posterior, and PCP-QERMit, an Importance Sampling method that is introduced to further decrease the numerical standard errors of the Value-at-Risk and Expected Shortfall estimators. The third main contribution is that we consider the effect of using a time-varying boundary of the region of interest. Extensive simulation and empirical studies show the ability of the introduced method to outperform standard approaches.",
keywords = "Bayesian inference, Censored likelihood, Censored posterior, Density forecasting, Expected Shortfall, Importance sampling, Markov chain Monte Carlo, Misspecification, Mixture of Student's t, Partially censored posterior, Value-at-Risk",
author = "Agnieszka Borowska and Lennart Hoogerheide and Koopman, {Siem Jan} and {van Dijk}, {Herman K.}",
year = "2020",
doi = "10.1016/j.jeconom.2019.12.007",
language = "English",
volume = "217",
pages = "335--355",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "2",

}

RIS

TY - JOUR

T1 - Partially censored posterior for robust and efficient risk evaluation

AU - Borowska, Agnieszka

AU - Hoogerheide, Lennart

AU - Koopman, Siem Jan

AU - van Dijk, Herman K.

PY - 2020

Y1 - 2020

N2 - A novel approach to inference for a specific region of the predictive distribution is introduced. An important domain of application is accurate prediction of financial risk measures, where the area of interest is the left tail of the predictive density of logreturns. Our proposed approach originates from the Bayesian approach to parameter estimation and time series forecasting, however it is robust in the sense that it provides a more accurate estimation of the predictive density in the region of interest in case of misspecification. The first main contribution of the paper is the novel concept of the Partially Censored Posterior (PCP), where the set of model parameters is partitioned into two subsets: for the first subset of parameters we consider the standard marginal posterior, for the second subset of parameters (that are particularly related to the region of interest) we consider the conditional censored posterior. The censoring means that observations outside the region of interest are censored: for those observations only the probability of being outside the region of interest matters. This quasi-Bayesian approach yields more precise parameter estimation than a fully censored posterior for all parameters, and has more focus on the region of interest than a standard Bayesian approach. The second main contribution is that we introduce two novel methods for computationally efficient simulation: Conditional MitISEM, a Markov chain Monte Carlo method to simulate model parameters from the Partially Censored Posterior, and PCP-QERMit, an Importance Sampling method that is introduced to further decrease the numerical standard errors of the Value-at-Risk and Expected Shortfall estimators. The third main contribution is that we consider the effect of using a time-varying boundary of the region of interest. Extensive simulation and empirical studies show the ability of the introduced method to outperform standard approaches.

AB - A novel approach to inference for a specific region of the predictive distribution is introduced. An important domain of application is accurate prediction of financial risk measures, where the area of interest is the left tail of the predictive density of logreturns. Our proposed approach originates from the Bayesian approach to parameter estimation and time series forecasting, however it is robust in the sense that it provides a more accurate estimation of the predictive density in the region of interest in case of misspecification. The first main contribution of the paper is the novel concept of the Partially Censored Posterior (PCP), where the set of model parameters is partitioned into two subsets: for the first subset of parameters we consider the standard marginal posterior, for the second subset of parameters (that are particularly related to the region of interest) we consider the conditional censored posterior. The censoring means that observations outside the region of interest are censored: for those observations only the probability of being outside the region of interest matters. This quasi-Bayesian approach yields more precise parameter estimation than a fully censored posterior for all parameters, and has more focus on the region of interest than a standard Bayesian approach. The second main contribution is that we introduce two novel methods for computationally efficient simulation: Conditional MitISEM, a Markov chain Monte Carlo method to simulate model parameters from the Partially Censored Posterior, and PCP-QERMit, an Importance Sampling method that is introduced to further decrease the numerical standard errors of the Value-at-Risk and Expected Shortfall estimators. The third main contribution is that we consider the effect of using a time-varying boundary of the region of interest. Extensive simulation and empirical studies show the ability of the introduced method to outperform standard approaches.

KW - Bayesian inference

KW - Censored likelihood

KW - Censored posterior

KW - Density forecasting

KW - Expected Shortfall

KW - Importance sampling

KW - Markov chain Monte Carlo

KW - Misspecification

KW - Mixture of Student's t

KW - Partially censored posterior

KW - Value-at-Risk

UR - http://www.scopus.com/inward/record.url?scp=85079396474&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2019.12.007

DO - 10.1016/j.jeconom.2019.12.007

M3 - Journal article

AN - SCOPUS:85079396474

VL - 217

SP - 335

EP - 355

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 2

ER -