Lennart F. Hoogerheide

VU University Amsterdam

De Boelelaan 1105

Amsterdam, ND North Holland 1081 HV

Netherlands

  • VU University Amsterdam

SCHOLARLY PAPERS

38

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Scholarly Papers (38)

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1.

Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations

The R Journal, Vol. 2, No. 2, pp. 41–47, 2010
Number of pages: 7 Posted: 21 Sep 2009 Last Revised: 08 Dec 2019
David Ardia and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences and VU University Amsterdam
Downloads 422 (134,469)

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GARCH, Bayesian, MCMC, Student-t, R software

2.

Efficient Bayesian Estimation and Combination of GARCH-Type Models

Rethinking Risk Measurement and Reporting: Examples and Applications from Finance, Vol. II, Chapter 1, Klaus Böcker, eds., RiskBooks, London, 2010
Number of pages: 22 Posted: 26 Jan 2010 Last Revised: 15 Nov 2017
David Ardia and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences and VU University Amsterdam
Downloads 405 (141,078)

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GARCH, Bayesian inference, MCMC, marginal likelihood, Bayesian model averaging, adaptive mixture of Student-t distributions, importance sampling

3.

Methods for Computing Numerical Standard Errors: Review and Application to Value-at-Risk Estimation

Journal of Time Series Econometrics, Vol. 10, No. 2, pp.1-9, 2018
Number of pages: 14 Posted: 07 Mar 2016 Last Revised: 03 Aug 2018
David Ardia, Keven Bluteau and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences, Université de Sherbrooke - Faculty of Administration and VU University Amsterdam
Downloads 350 (165,842)
Citation 1

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Bootstrap, GARCH, HAC kernel, numerical standard error (NSE), Monte Carlo, Markov chain Monte Carlo (MCMC), spectral density, Value-at-Risk precision

4.

Return and Risk of Pairs Trading Using a Simulation-Based Bayesian Procedure for Predicting Stable Ratios of Stock Prices

Tinbergen Institute Discussion Paper 14-039/III
Number of pages: 34 Posted: 26 Mar 2014 Last Revised: 29 Oct 2014
Lukasz T. Gatarek, Lennart F. Hoogerheide and H. K. van Dijk
Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE), VU University Amsterdam and Tinbergen Institute
Downloads 340 (171,124)
Citation 3

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Bayesian analysis; cointegration; linear normalization; orthogonal normalization; pairs trading; statistical arbitrage

5.

Bayesian Forecasting of Value at Risk and Expected Shortfall Using Adaptive Importance Sampling

Tinbergen Institute Discussion Paper No. TI 2008-092/4
Number of pages: 38 Posted: 03 Oct 2008
Lennart F. Hoogerheide and H. K. van Dijk
VU University Amsterdam and Tinbergen Institute
Downloads 309 (189,440)
Citation 7

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Value at Risk, Expected Shortfall, numerical accuracy, numerical standard error, importance sampling, mixture of Student-t distributions, variance reduction technique

6.

Time-Varying Combinations of Bayesian Dynamic Models and Equity Momentum Strategies

Tinbergen Institute Discussion Paper 16-099/III
Number of pages: 44 Posted: 22 Nov 2016
Nalan Basturk, Stefano Grassi, Lennart F. Hoogerheide and H. K. van Dijk
Maastricht University - Department of Quantitative Economics, University of Kent - Canterbury Campus, VU University Amsterdam and Tinbergen Institute
Downloads 287 (204,752)

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nonlinear, non-gaussian state space, filters, density combinations, bayesian modeling, equity momentum

7.

Education and Entrepreneurial Choice: An Instrumental Variables Analysis

International Small Business Journal, Vol. 31(1), pp. 23-33, 2013
Number of pages: 15 Posted: 14 Oct 2009 Last Revised: 20 Apr 2013
Jorn H. Block, Lennart F. Hoogerheide, Roy Thurik and Roy Thurik
University of Trier - Faculty of Management, VU University Amsterdam and Erasmus University Rotterdam (EUR) - Centre for Advanced Small Business Economics (CASBEC)Montpellier Business School
Downloads 243 (241,868)
Citation 2

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Occupational choice, entrepreneurial choice, education, self-employment, endogeneity, instrumental variables, entrepreneurship

8.

Simulation Based Bayesian Econometric Inference: Principles and Some Recent Computational Advances

CORE Discussion Paper No. 2007/15
Number of pages: 61 Posted: 25 Jun 2007
Lennart F. Hoogerheide, H. K. van Dijk and R.D. van Oest
VU University Amsterdam, Tinbergen Institute and Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE)
Downloads 237 (247,934)
Citation 4

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9.

Bayesian Risk Forecasting for Long Horizons

Tinbergen Institute Discussion Paper 2019-018/III
Number of pages: 40 Posted: 13 Mar 2019
Agnieszka Borowska, Lennart F. Hoogerheide and Siem Jan Koopman
VU University Amsterdam, VU University Amsterdam and Vrije Universiteit Amsterdam - School of Business and Economics
Downloads 201 (289,289)

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Bayesian inference, forecasting, importance sampling, numerical accuracy, long run risk, Value-at-Risk, Expected Shortfall

10.

Are Education and Entrepreneurial Income Endogenous? A Bayesian Analysis

Entrepreneurship Research Journal, 2(3), 2012
Number of pages: 21 Posted: 20 Mar 2010 Last Revised: 01 Mar 2014
Jorn H. Block, Lennart F. Hoogerheide, Roy Thurik and Roy Thurik
University of Trier - Faculty of Management, VU University Amsterdam and Erasmus University Rotterdam (EUR) - Centre for Advanced Small Business Economics (CASBEC)Montpellier Business School
Downloads 190 (304,472)
Citation 2

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Education, income, entrepreneurship, self-employment, endogeneity, instrumental variables, Bayesian analysis

11.

Forecast Accuracy and Economic Gains from Bayesian Model Averaging Using Time Varying Weights

Tinbergen Institute Discussion Paper 09-061/4
Number of pages: 28 Posted: 17 Jul 2009
Lennart F. Hoogerheide, Richard Kleijn, Francesco Ravazzolo, H. K. van Dijk and Marno Verbeek
VU University Amsterdam, affiliation not provided to SSRN, Free University of Bozen-Bolzano - Faculty of Economics and Management, Tinbergen Institute and Erasmus University - Rotterdam School of Management
Downloads 171 (334,485)
Citation 18

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forecast combination, Bayesian model averaging, time varying model weights, portfolio optimization, business cycle

12.

Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit

Journal of Statistical Software, Vol. 29, No. 3, pp.1-32, Jan 2009
Number of pages: 32 Posted: 23 Jun 2008 Last Revised: 03 Aug 2018
David Ardia, Lennart F. Hoogerheide and H. K. van Dijk
HEC Montreal - Department of Decision Sciences, VU University Amsterdam and Tinbergen Institute
Downloads 169 (337,928)
Citation 1

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adaptive mixture, Student-t distributions, importance sampling, independence chain Metropolis-Hasting algorithm, Bayesian, R software

13.

Backtesting Value-at-Risk Using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann

Tinbergen Institute Discussion Paper 11-131/4
Number of pages: 17 Posted: 20 Sep 2011
Lennart F. Hoogerheide, Francesco Ravazzolo and H. K. van Dijk
VU University Amsterdam, Free University of Bozen-Bolzano - Faculty of Economics and Management and Tinbergen Institute
Downloads 145 (383,776)
Citation 2

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value-at-Risk, backtest, optimal revision, forecast rationality

14.

GARCH Models for Daily Stock Returns: Impact of Estimation Frequency on Value-at-Risk and Expected Shortfall Forecasts

Downloads 142 (390,176)
Citation 1

GARCH Models for Daily Stock Returns: Impact of Estimation Frequency on Value-at-Risk and Expected Shortfall Forecasts

Tinbergen Institute Discussion Paper 2013-047/III
Number of pages: 18 Posted: 21 Mar 2013
David Ardia and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences and VU University Amsterdam
Downloads 142 (390,818)
Citation 1

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GARCH, Value-at-Risk, Expected Shortfall, equity, frequency, false discovery rate

GARCH Models for Daily Stock Returns: Impact of Estimation Frequency on Value-at-Risk and Expected Shortfall Forecasts

Economics Letters, Vol. 123, Issue 2, pp.187-190, May 2014
Posted: 27 Feb 2013 Last Revised: 11 Mar 2014
David Ardia and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences and VU University Amsterdam

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GARCH, Value-at-Risk, Expected Shortfall, equity, frequency, estimation, false discovery rate

15.

The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference

Downloads 135 (405,905)

The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference

Tinbergen Institute Discussion Paper 15-042/III
Number of pages: 43 Posted: 31 Mar 2015 Last Revised: 08 Jul 2017
Nalan Basturk, Stefano Grassi, Lennart F. Hoogerheide, Anne Opschoor and H. K. van Dijk
Maastricht University - Department of Quantitative Economics, University of Kent - Canterbury Campus, VU University Amsterdam, Vrije Universiteit Amsterdam and Tinbergen Institute
Downloads 86 (564,852)

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finite mixtures, Student-t densities, importance sampling, MCMC, Metropolis-Hastings algorithm, expectation maximization, Bayesian inference, R-software

The R Package Mitisem: Efficient and Robust Simulation Procedures for Bayesian Inference

Norges Bank Working Paper 10/2017
Number of pages: 43 Posted: 19 Jul 2017
Nalan Basturk, Stefano Grassi, Lennart F. Hoogerheide, Anne Opschoor and H. K. van Dijk
Maastricht University - Department of Quantitative Economics, University of Kent - Canterbury Campus, VU University Amsterdam, Vrije Universiteit Amsterdam and Tinbergen Institute
Downloads 49 (760,500)

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finite mixtures, Student-t densities, importance sampling, MCMC, MetropolisHastings algorithm, expectation maximization, Bayesian inference, R software

16.

Censored Posterior and Predictive Likelihood in Bayesian Left-Tail Prediction for Accurate Value at Risk Estimation

Tinbergen Institute Discussion Paper 13-060/III
Number of pages: 37 Posted: 17 Apr 2013 Last Revised: 10 Mar 2014
Lukasz T. Gatarek, Lennart F. Hoogerheide, Koen Hooning and H. K. van Dijk
Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE), VU University Amsterdam, Delft University of Technology and Tinbergen Institute
Downloads 133 (410,829)
Citation 5

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censored likelihood, censored posterior, censored predictive likelihood, Bayesian Model Averaging, Value at Risk, Metropolis-Hastings algorithm

17.

Family Background Variables as Instruments for Education in Income Regressions: A Bayesian Analysis

Economics of Education Review, Vol. 31, Issue 5, pp. 515-523
Number of pages: 18 Posted: 15 Aug 2010 Last Revised: 05 Jan 2013
Lennart F. Hoogerheide, Jorn H. Block, Roy Thurik and Roy Thurik
VU University Amsterdam, University of Trier - Faculty of Management and Erasmus University Rotterdam (EUR) - Centre for Advanced Small Business Economics (CASBEC)Montpellier Business School
Downloads 133 (410,829)
Citation 5

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education, family background variables, earnings, income, instrumental variables, Bayesian analysis

18.

The R Package Mitlsem: Mixture of Student-T Distributions Using Importance Sampling Weighted Expectation Maximization for Efficient and Robust Simulation

Tinbergen Institute Discussion Paper TI 12-096/III
Number of pages: 32 Posted: 22 Sep 2012
Nalan Basturk, Lennart F. Hoogerheide, Anne Opschoor and H. K. van Dijk
Maastricht University - Department of Quantitative Economics, VU University Amsterdam, Vrije Universiteit Amsterdam and Tinbergen Institute
Downloads 130 (418,082)
Citation 3

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finite mixtures, Student-t distributions, Importance Sampling, MCMC, Metropolis-Hastings algorithm, Expectation Maximization, Bayesian inference, R software

19.

To Bridge, to Warp or to Wrap? A Comperative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood

Computational Statistics & Data Analysis, Vol. 56, No. 11, pp. 3398-3414, 2012, TI Discussion Paper No. 09-017/4
Number of pages: 44 Posted: 26 Feb 2009 Last Revised: 13 May 2015
David Ardia, Lennart F. Hoogerheide and H. K. van Dijk
HEC Montreal - Department of Decision Sciences, VU University Amsterdam and Tinbergen Institute
Downloads 123 (436,090)
Citation 1

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marginal likelihood, Bayes factor, importance sampling, Markov chain Monte Carlo, bridge sampling, adaptive mixture of Student-t distributions

20.

AdMit: Adaptive Mixtures of Student-t Distributions

The R Journal, Vol. 1, No. 1, pp. 25-30, May 2009
Number of pages: 6 Posted: 16 Jun 2010 Last Revised: 03 Aug 2018
David Ardia, Lennart F. Hoogerheide and H. K. van Dijk
HEC Montreal - Department of Decision Sciences, VU University Amsterdam and Tinbergen Institute
Downloads 117 (452,829)

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adaptive mixture, Student-t distributions, importance sampling, independence chain Metropolis-Hasting algorithm, Bayesian, R software

21.

Cross-Sectional Distribution of GARCH Coefficients across S&P 500 Constituents: Time-Variation over the Period 2000-2012

Wilmott Magazine, Issue 66, pp. 40-44, July 2013
Number of pages: 9 Posted: 02 Mar 2013 Last Revised: 23 Nov 2017
David Ardia and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences and VU University Amsterdam
Downloads 108 (480,432)

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GARCH, GJR, equity, leverage effect, S&P 500 universe

22.

Bayesian Analysis of Instrumental Variable Models: Acceptance-Rejection within Direct Monte Carlo

Tinbergen Institute Discussion Paper 12-098/III
Number of pages: 35 Posted: 27 Sep 2012
Arnold Zellner, Tomohiro Ando, Nalan Basturk, Lennart F. Hoogerheide and H. K. van Dijk
University of Chicago, Booth School of Business (Deceased), University of Melbourne - Melbourne Business School, Maastricht University - Department of Quantitative Economics, VU University Amsterdam and Tinbergen Institute
Downloads 96 (520,949)

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Instrumental variables, Bayesian inference, Direct Monte Carlo, Acceptance-Rejection, numerical standard errors

23.

A Class of Adaptive EM-Based Importance Sampling Algorithms for Efficient and Robust Posterior and Predictive Simulation

Tinbergen Institute Discussion Paper No. 2011-004/4
Number of pages: 53 Posted: 10 Jan 2011
Lennart F. Hoogerheide, Anne Opschoor and H. K. van Dijk
VU University Amsterdam, Vrije Universiteit Amsterdam and Tinbergen Institute
Downloads 96 (520,949)
Citation 6

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Mixture of Student-T Distributions, Importance Sampling, Kullback-Leibler Divergence, Expectation Maximization, Metropolis-Hastings Algorithm, Predictive Likelihoods, Mixture GARCH Models, Value at Risk

24.

A Class of Adaptive Importance Sampling Weighted EM Algorithms for Efficient and Robust Posterior and Predictive Simulation

Tinbergen Institute Discussion Paper No. 12-026/4
Number of pages: 37 Posted: 25 Mar 2012
Lennart F. Hoogerheide, Anne Opschoor and H. K. van Dijk
VU University Amsterdam, Vrije Universiteit Amsterdam and Tinbergen Institute
Downloads 90 (542,907)
Citation 2

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mixture of Student-t distributions, importance sampling, Kullback-Leibler divergence, Expectation Maximization, Metropolis-Hastings algorithm, predictive likelihood, DCC GARCH, mixture GARCH, instrumental variables

25.

Possibly Ill-Behaved Posteriors in Econometric Models

Tinbergen Institute Discussion Paper No. 08-036/4
Number of pages: 44 Posted: 08 Apr 2008
Lennart F. Hoogerheide and H. K. van Dijk
VU University Amsterdam and Tinbergen Institute
Downloads 89 (546,731)
Citation 3

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instrumental variables, vector error correction model, mixture model, importance sampling, Markov chain Monte Carlo, neural network

26.

Joint Bayesian Analysis of Parameters and States in Nonlinear, Non-Gaussian State Space Models

Tinbergen Institute Discussion Paper 14-118/III
Number of pages: 35 Posted: 02 Sep 2014 Last Revised: 31 Mar 2016
Istvan Barra, Lennart F. Hoogerheide, Siem Jan Koopman and Andre Lucas
VU University Amsterdam, VU University Amsterdam, Vrije Universiteit Amsterdam - School of Business and Economics and Vrije Universiteit Amsterdam
Downloads 85 (562,390)
Citation 1

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Bayesian inference, importance sampling, Monte Carlo estimation, Metropolis-Hastings algorithm, mixture of student's t-distributions

27.

On the Shape of Posterior Densities and Credible Sets in Instrumental Variable Regression Models with Reduced Rank: An Application of Flexible Sampling Methods Using Neural Networks

CORE Discussion Paper No. 2005/29
Number of pages: 35 Posted: 27 Jan 2006
Lennart F. Hoogerheide, Johan F. kaashoek and H. K. van Dijk
VU University Amsterdam, Erasmus University Rotterdam (EUR) and Tinbergen Institute
Downloads 83 (570,413)
Citation 5

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instrumental variables, reduced rank, importance sampling, Markov chain Monte Carlo, neural networks, Bayesian inference, credible sets

28.

Forecast Density Combinations of Dynamic Models and Data Driven Portfolio Strategies

Tinbergen Institute Discussion Paper 2018-076/III
Number of pages: 53 Posted: 04 Nov 2018
Nalan Basturk, Agnieszka Borowska, Stefano Grassi, Lennart F. Hoogerheide and H. K. van Dijk
Maastricht University - Department of Quantitative Economics, VU University Amsterdam, University of Rome Tor Vergata, VU University Amsterdam and Tinbergen Institute
Downloads 76 (599,969)
Citation 1

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forecast combination, momentum strategy, filtering methods, Bayes estimates

29.

Bayesian Analysis of Boundary and Near-Boundary Evidence in Econometric Models with Reduced Rank

Downloads 74 (608,945)

Bayesian Analysis of Boundary and Near-Boundary Evidence in Econometric Models with Reduced Rank

Tinbergen Institute Discussion Paper No. 17-058/III
Number of pages: 91 Posted: 29 Jun 2017
Nalan Basturk, Lennart F. Hoogerheide and H. K. van Dijk
Maastricht University - Department of Quantitative Economics, VU University Amsterdam and Tinbergen Institute
Downloads 41 (818,632)

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Bayesian Analysis, Reduced Rank, Lasso Priors, Shrinkage, Bayesian Mixtures

Bayesian Analysis of Boundary and Near-Boundary Evidence in Econometric Models with Reduced Rank

Norges Bank Working Paper 11/17
Number of pages: 91 Posted: 08 Sep 2017
Nalan Basturk, Lennart F. Hoogerheide and H. K. van Dijk
Maastricht University - Department of Quantitative Economics, VU University Amsterdam and Tinbergen Institute
Downloads 33 (885,389)

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30.

Stock Index Returns' Density Prediction Using GARCH Models: Frequentist or Bayesian Estimation?

Economics Letters, Vol. 116, pp. 322-325, September 2012
Number of pages: 6 Posted: 20 Jan 2011 Last Revised: 17 Nov 2017
Lennart F. Hoogerheide, David Ardia and Nienké Corré
VU University Amsterdam, HEC Montreal - Department of Decision Sciences and Bain & Company - Bain & Company, Netherlands, LLC
Downloads 63 (662,737)
Citation 1

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GARCH, Bayesian, KLIC, censored likelihood

31.

Learning to Average Predictively Over Good and Bad: Comment on: Using Stacking to Average Bayesian Predictive Distributions

Tinbergen Institute Discussion Paper 2018-063/III
Number of pages: 9 Posted: 20 Aug 2018
Lennart F. Hoogerheide and H. K. van Dijk
VU University Amsterdam and Tinbergen Institute
Downloads 56 (700,757)

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Bayesian learning, predictive density combinations

32.

Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM

Tinbergen Institute Discussion Paper 16-005/III
Number of pages: 26 Posted: 25 Jan 2016
Nalan Basturk, Stefano Grassi, Lennart F. Hoogerheide and H. K. van Dijk
Maastricht University - Department of Quantitative Economics, University of Kent - Canterbury Campus, VU University Amsterdam and Tinbergen Institute
Downloads 42 (790,573)

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finite mixtures, Student-t distributions, Importance Sampling, MCMC, Metropolis-Hastings algorithm, Expectation Maximization, Bayesian inference

33.

Partially Censored Posterior for Robust and Efficient Risk Evaluation

Tinbergen Institute Discussion Paper 2019-057/III
Number of pages: 33 Posted: 22 Aug 2019
Agnieszka Borowska, Lennart F. Hoogerheide, Siem Jan Koopman and Herman van Dijk
VU University Amsterdam, VU University Amsterdam, Vrije Universiteit Amsterdam - School of Business and Economics and Tinbergen Institute
Downloads 35 (843,884)
Citation 1

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Bayesian Inference, Censored Likelihood, Censored Posterior, Partially Censored Posterior, Misspecification, Density Forecasting, Markov Chain Monte Carlo, Importance Sampling, Mixture of Student's T, Value-At-Risk, Expected Shortfall

34.

A Note on Jointly Backtesting Models for Multiple Assets and Horizons

Wilmott Magazine 83, pp.46-48, 2016
Number of pages: 6 Posted: 13 Feb 2016 Last Revised: 15 Nov 2017
David Ardia, Anas Guerrouaz and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences, Université Laval - Département de Finance et Assurance and VU University Amsterdam
Downloads 35 (843,884)

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Bootstrap test, GARCH, dependent time series, multiple testing, Value-at-Risk

35.

Worldwide Equity Risk Prediction

Applied Economics Letters, Vol. 20, No. 14, 2013
Number of pages: 9 Posted: 23 May 2012 Last Revised: 14 Nov 2017
David Ardia and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences and VU University Amsterdam
Downloads 31 (877,801)

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GARCH, value-at-risk, equity, worldwide, false discovery rate

36.

Bayes estimates of multimodal density features using DNA and Economic Data

Tinbergen Institute Discussion Paper 2021-017/III
Number of pages: 33 Posted: 18 Feb 2021
Nalan Basturk, Lennart F. Hoogerheide and Herman van Dijk
Maastricht University - Department of Quantitative Economics, VU University Amsterdam and Tinbergen Institute
Downloads 30 (886,520)

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Multimodality, mixtures, Markov Chain Monte Carlo, Bayesian Inference

37.

Flexible Negative Binomial Mixtures for Credible Mode Inference in Heterogeneous Count Data from Finance, Economics and Bioinformatics

Number of pages: 29 Posted: 02 Sep 2024
Jamie Cross, Jamie Cross, Lennart F. Hoogerheide, Paul Labonne and H. K. van Dijk
Australian National University (ANU) - Centre for Applied Macroeconomic Analysis (CAMA)Center of Applied Macroeconomics and Commodity Prices (CAMP), BI Norwegian Business School, VU University Amsterdam, BI Norwegian Business School and Tinbergen Institute
Downloads 10 (1,091,215)

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multimodality, mixtures, shifted negative binomial, Markov chain Monte Carlo, sparse finite mixture.

38.

A New Bootstrap Test for Multiple Assets Joint Risk Testing

Journal of Risk, 2017, Volume 19, Issue 4, pages 1-22
Posted: 19 Aug 2013 Last Revised: 14 Nov 2017
David Ardia, Lukasz T. Gatarek and Lennart F. Hoogerheide
HEC Montreal - Department of Decision Sciences, Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) and VU University Amsterdam

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Bootstrap test, GARCH, marginal models, multiple time series, Value-at-Risk