Sequential Monte Carlo with model tempering
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Marko Mlikota
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Frank Schorfheide
Abstract
Modern macroeconometrics often relies on time series models for which it is time-consuming to evaluate the likelihood function. We demonstrate how Bayesian computations for such models can be drastically accelerated by reweighting and mutating posterior draws from an approximating model that allows for fast likelihood evaluations, into posterior draws from the model of interest, using a sequential Monte Carlo (SMC) algorithm. We apply the technique to the estimation of a vector autoregression with stochastic volatility and two nonlinear dynamic stochastic general equilibrium models. The runtime reductions we obtain range from 27 % to 88 %.
Funding source: National Science Foundation
Award Identifier / Grant number: SES 1851634
Acknowledgement
We thank Marco Del Negro, David Childers, and seminar and conference participants at Penn, the 2021 Conference of Swiss Economists Abroad, the 2022 Barcelona GSE Summer Forum, the 2022 Annual Conference of the IAAE in London, the 2022 ESOBE Meetings in Salzburg, and the 2022 FRB Philadelphia Conference on Frontiers in Machine Learning and Economics for helpful comments and discussions.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: Schorfheide gratefully acknowledges financial support from the National Science Foundation under Grant SES 1851634.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Acharya, S., W. Chen, M. Del Negro, K. Dogra, E. Matlin, and R. Sarfati. 2021. “Estimating HANK: Macro Time Series and Micro Moments.” In Working Paper. Federal Reserve Bank of New York.Suche in Google Scholar
Aruoba, B., L. Bocola, and F. Schorfheide. 2017. “Assessing DSGE Model Nonlinearities.” Journal of Economic Dynamics and Control 83: 34–54. https://doi.org/10.1016/j.jedc.2017.07.006.Suche in Google Scholar
Aruoba, B., M. Mlikota, F. Schorfheide, and S. Villalvazo. 2022. “SVARs with Occasionally-Binding Constraints.” Journal of Econometrics. forthcoming. https://doi.org/10.1016/j.jeconom.2021.07.013.Suche in Google Scholar
Bon, J. J., A. Lee, and C. Drovandi. 2021. “Accelerating Sequential Monte Carlo with Surrogate Likelihoods.” Statistics and Computing 31: 1–26. https://doi.org/10.1007/s11222-021-10036-4.Suche in Google Scholar
Cai, M., M. Del Negro, E. Herbst, E. Matlin, R. Sarfati, and F. Schorfheide. 2021. “Online Estimation of DSGE Models.” The Econometrics Journal 24: C33–58. https://doi.org/10.1093/ectj/utaa029.Suche in Google Scholar
Chopin, N. 2002. “A Sequential Particle Filter for Static Models.” Biometrika 89: 539–51. https://doi.org/10.1093/biomet/89.3.539.Suche in Google Scholar
Chopin, N., P. E. Jacob, and O. Papaspiliopoulos. 2013. “SMC2: An Efficient Algorithm for Sequential Analysis of State Space Models.” Journal of the Royal Statistical Society: Series B 75: 397–426. https://doi.org/10.1111/j.1467-9868.2012.01046.x.Suche in Google Scholar
Christen, A. J., and C. Fox. 2005. “Markov Chain Monte Carlo Using an Approximation.” Journal of Computational & Graphical Statistics 14: 795–810. https://doi.org/10.1198/106186005x76983.Suche in Google Scholar
Creal, D. 2007. Sequential Monte Carlo Samplers for Bayesian DSGE Models.Notre Dame. Notre Dame: University of Notre Dame.Suche in Google Scholar
Dai, C., J. Heng, P. E. Jacob, and N. Whiteley. 2022. “An Invitation to Sequential Monte Carlo Samplers.” Journal of the American Statistical Association 117: 1587–600. https://doi.org/10.1080/01621459.2022.2087659.Suche in Google Scholar
Del Moral, P., A. Doucet, and A. Jasra. 2012. “An Adaptive Sequential Monte Carlo Method for Approximate Bayesian Computation.” Statistical Computing 22: 1009–20. https://doi.org/10.1007/s11222-011-9271-y.Suche in Google Scholar
Doppelt, R., and K. O’Hara. 2020. “Bayesian Estimation of Fractionally Integrated Vector Autoregressions and an Application to Identified Technology Shocks.” In Working Paper. Penn State University.Suche in Google Scholar
Durham, G., and J. Geweke. 2014. “Adaptive Sequential Posterior Simulators for Massively Parallel Computing Environments.” In Advances in Econometrics, Vol. 34, edited by I. Jeliazkov, and D. Poirier, 1–44. West Yorkshire: Emerald Group Publishing Limited. chap. 6.10.1108/S0731-905320140000034003Suche in Google Scholar
Geweke, J. 1989. “Bayesian Inference in Econometrics Models Using Monte Carlo Integration.” Econometrica 57: 1317–39. https://doi.org/10.2307/1913710.Suche in Google Scholar
Geweke, J. 2014. Exact Optimization by Means of Sequentially Adaptive Bayesian Learning. Seattle: University of Iowa. Manuscript.Suche in Google Scholar
Gordon, N., D. Salmond, and A. F. Smith. 1993. “Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation.” Radar and Signal Processing, IEE Proceedings F 140: 107–13. https://doi.org/10.1049/ip-f-2.1993.0015.Suche in Google Scholar
Herbst, E., and F. Schorfheide. 2014. “Sequential Monte Carlo Sampling for DSGE Models.” Journal of Applied Econometrics 29: 1073–98. https://doi.org/10.1002/jae.2397.Suche in Google Scholar
Herbst, E., and F. Schorfheide. 2015. Bayesian Estimation of DSGE Models. Princeton: Princeton University Press.10.23943/princeton/9780691161082.001.0001Suche in Google Scholar
Herbst, E., and F. Schorfheide. 2019. “Tempered Particle Filtering.” Journal of Econometrics 210: 26–44. https://doi.org/10.1016/j.jeconom.2018.11.003.Suche in Google Scholar
Hoogerheide, L., A. Opschoor, and H. van Dijk. 2012. “A Class of Adaptive Importance Sampling Weighted EM Algorithms for Efficient and Robust Posterior and Predictive Simulation.” Journal of Econometrics 171: 101–20. https://doi.org/10.1016/j.jeconom.2012.06.011.Suche in Google Scholar
Jasra, A., D. A. Stephens, A. Doucet, and T. Tsagaris. 2011. “Inference for Levy-Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo.” Scandinavian Journal of Statistics 38: 1–22. https://doi.org/10.1111/j.1467-9469.2010.00723.x.Suche in Google Scholar
Kim, S., N. Shephard, and S. Chib. 1998. “Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models.” The Review of Economic Studies 65: 361–93. https://doi.org/10.1111/1467-937x.00050.Suche in Google Scholar
Kloek, T., and H. K. van Dijk. 1978. “Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo.” Econometrica 46: 1–19. https://doi.org/10.2307/1913641.Suche in Google Scholar
Liu, J. S. 2001. Monte Carlo Strategies in Scientific Computing. New York: Springer.Suche in Google Scholar
Mathews, J., and S. C. Schmidler. 2022. “Finite Sample Complexity of Sequential Mote Carlo Estimators on Multimodal Target Distributions.” arXiv Working Paper 2208.06672.Suche in Google Scholar
Schäfer, C., and N. Chopin. 2013. “Sequential Monte Carlo on Large Binary Sampling Spaces.” Statistical Computing 23: 163–84. https://doi.org/10.1007/s11222-011-9299-z.Suche in Google Scholar
Smets, F., and R. Wouters. 2007. “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach.” The American Economic Review 97: 586–606. https://doi.org/10.1257/aer.97.3.586.Suche in Google Scholar
Smith, M. 2011. “Estimating Nonlinear Economics Models Using Surrogate Transitions.” In Working Paper. Federal Reserve Board.Suche in Google Scholar
Zhou, Y., A. M. Johansen, and J. A. Aston. 2015. “Towards Automatic Model Comparison: An Adaptive Sequential Monte Carlo Approach.” arXiv Working Paper, 1303.3123v2.Suche in Google Scholar
Supplementary Material
This article contains supplementary material (https://doi.org/10.1515/snde-2022-0103).
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Editorial
- Editorial Introduction of the Special Issue of Studies in Nonlinear Dynamics and Econometrics in Honor of Herman van Dijk
- Review
- Challenges and Opportunities for Twenty First Century Bayesian Econometricians: A Personal View
- Research Articles
- Markov-Switching Models with Unknown Error Distributions: Identification and Inference Within the Bayesian Framework
- Dynamic Shrinkage Priors for Large Time-Varying Parameter Regressions Using Scalable Markov Chain Monte Carlo Methods
- Matrix autoregressive models: generalization and Bayesian estimation
- Sequential Monte Carlo with model tempering
- Modeling Corporate CDS Spreads Using Markov Switching Regressions
- Combining Large Numbers of Density Predictions with Bayesian Predictive Synthesis
- Bayesian inference for non-anonymous growth incidence curves using Bernstein polynomials: an application to academic wage dynamics
- Bayesian Reconciliation of Return Predictability
- A Dynamic Latent-Space Model for Asset Clustering
- Posterior Manifolds over Prior Parameter Regions: Beyond Pointwise Sensitivity Assessments for Posterior Statistics from MCMC Inference
- Bayesian Flexible Local Projections
Artikel in diesem Heft
- Frontmatter
- Editorial
- Editorial Introduction of the Special Issue of Studies in Nonlinear Dynamics and Econometrics in Honor of Herman van Dijk
- Review
- Challenges and Opportunities for Twenty First Century Bayesian Econometricians: A Personal View
- Research Articles
- Markov-Switching Models with Unknown Error Distributions: Identification and Inference Within the Bayesian Framework
- Dynamic Shrinkage Priors for Large Time-Varying Parameter Regressions Using Scalable Markov Chain Monte Carlo Methods
- Matrix autoregressive models: generalization and Bayesian estimation
- Sequential Monte Carlo with model tempering
- Modeling Corporate CDS Spreads Using Markov Switching Regressions
- Combining Large Numbers of Density Predictions with Bayesian Predictive Synthesis
- Bayesian inference for non-anonymous growth incidence curves using Bernstein polynomials: an application to academic wage dynamics
- Bayesian Reconciliation of Return Predictability
- A Dynamic Latent-Space Model for Asset Clustering
- Posterior Manifolds over Prior Parameter Regions: Beyond Pointwise Sensitivity Assessments for Posterior Statistics from MCMC Inference
- Bayesian Flexible Local Projections
