Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

5 Issues per year


IMPACT FACTOR 2017: 0.855

CiteScore 2017: 0.76

SCImago Journal Rank (SJR) 2017: 0.668
Source Normalized Impact per Paper (SNIP) 2017: 0.894

Mathematical Citation Quotient (MCQ) 2017: 0.02

Online
ISSN
1558-3708
See all formats and pricing
More options …
Volume 19, Issue 5

Issues

Particle Gibbs with ancestor sampling for stochastic volatility models with: heavy tails, in mean effects, leverage, serial dependence and structural breaks

Nima Nonejad
  • Corresponding author
  • Aarhus University and Creates – Department of Economics and Business, Fuglesangs Alle 4, Aarhus 8210, Aarhus V, Denmark
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-04-21 | DOI: https://doi.org/10.1515/snde-2014-0043

Abstract

Particle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of stochastic volatility models with increasing complexity, including leverage and in mean effects. We provide applications that demonstrate the flexibility of PG-AS under these different circumstances and justify applying it in practice. We also combine discrete structural breaks within the stochastic volatility model framework. For instance, we model changing time series characteristics of monthly postwar US core inflation rate using a structural break autoregressive fractionally integrated moving average (ARFIMA) model with stochastic volatility. We allow for structural breaks in the level, long and short-memory parameters with simultaneous breaks in the level, persistence and the conditional volatility of the volatility of inflation.

This article offers supplementary material which is provided at the end of the article.

Keywords: ancestor sampling; Bayes; particle filtering; structural breaks

JEL Classification:: C11; C22; C52; C63

References

  • Abanto-Valle, C. A., D. Bandyopadhyay, V. H. Lachos, and I. Enriquez. 2010. “Robust Bayesian Analysis of Heavy-Tailed Stochastic Volatility Models Using Scale Mixtures of Normal Distributions.” Computational Statistics and Data Analysis 54 (12): 2883–2898.Web of ScienceCrossrefGoogle Scholar

  • Andrieu, C., and A. Doucet. 2002. “Particle Filtering for Partially Observed Gaussian State Space Models.” Journal of the Royal Statistical Society B 64 (4): 827–836.Google Scholar

  • Andrieu, C., A. Doucet, and R. Holenstein. 2010. “Particle Markov chain Monte Carlo methods (with discussion).” Journal of the Royal Statistical Society B 72 (3): 1–33.Google Scholar

  • Bauwens, L., G. Koop, D. Korobilis, and V. K. Rombouts. 2011. “A Comparison of Forecasting Models for Macroeconomics Series: The Contribution of Structural Break Models.” Working paper, University of Strathclyde.Google Scholar

  • Berg, A., R. Meyer, and J. Yu. 2004. “Deviance Information Criterion for Comparing Stochastic Volatility Models.” Journal of Business and Economic Statistics 22 (1): 107–120.Google Scholar

  • Bollerslev, T. 1987. “A Conditional Heteroskedastic Time Series Model for Speculative Prices and Rates of Return.” The Review of Economics and Statistics 69 (3): 542–547.CrossrefGoogle Scholar

  • Bos, C. S., S. J. Koopman, and M. Ooms. 2012. “Long Memory with Stochastic Variance Model: A Recursive Analysis for U.S. Inflation.” Computational Statistics and Data Analysis 76 (3): 144–157.Web of ScienceCrossrefGoogle Scholar

  • Chan, J. 2013. “Moving Average Stochastic Volatility Models with Application to Inflation Forecast.” Journal of Econometrics 176 (2): 162–172.Web of ScienceCrossrefGoogle Scholar

  • Chan, J. 2014. “The Stochastic Volatility in Mean Model with Time-Varying Parameters: An Application to Inflation Modeling.” Working paper, Research School of Economics, Australian National University.Google Scholar

  • Chan, J., and A. L. Grant. 2014. “Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion.” Working paper, Research School of Economics, Australian National University.Google Scholar

  • Chan, J., and C. Hsiao. 2013. “Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence.” In Bayesian Inference in the Social Sciences, edited by I. Jeliazkov, and X.-S. Yang (Eds.). 159–180, Hoboken, New Jersey: John Wiley & Sons.Google Scholar

  • Chan, N. H., and W. Palma. 1998. “State Space Modeling of Long-Memory Processes.” Annals of Statistics 26 (2): 719–740.CrossrefGoogle Scholar

  • Chib, S. 1995. “Marginal Likelihood from the Gibbs Output.” Journal of the American Statistical Association 90 (432): 1313–1321.CrossrefGoogle Scholar

  • Chib, S. 1998. “Estimation and Comparison of Multiple Change-Point Models.” Journal of Econometrics 86 (2): 221–241.CrossrefGoogle Scholar

  • Chib, S., and E. Greenberg. 1995. “Understanding the Metropolis-Hastings Algorithm.” The American Statistician 49 (4): 327–335.Google Scholar

  • Chib, S., F. Nadari, and N. Shephard. 2002. “Markov Chain Monte Carlo Methods for Stochastic Volatility Models.” Journal of Econometrics 108 (2): 281–316.CrossrefWeb of ScienceGoogle Scholar

  • Cogley, T., and T. J. Sargent. 2005. “Drifts and Volatilities: Monetary Policies and Outcomes in the Post WWII US.” Review of Economic Dynamics 8 (2): 262–302.CrossrefGoogle Scholar

  • Doucet, A., and A. Johansen. 2011. “A Tutorial on Particle Filtering and Smoothing: Fifteen Years Later.” In The Oxford Handbook of Nonlinear Filtering, edited by D. Crisan, and B. Rozovsky. New York: Oxford University Press.Google Scholar

  • Eisenstat, E., and R. W. Strachan. 2014. “Modelling Inflation Volatility.” CAMA Working Paper 24.Google Scholar

  • Flury, T., and N. Shephard. 2011. “Bayesian Inference Based Only on Simulated Likelihood: Particle Filter Analysis of Dynamic Economic Models.” Econometric Theory 27 (5): 933–956.CrossrefWeb of ScienceGoogle Scholar

  • Gelfand, A., and D. Dey. 1994. “Bayesian Model Choice: Asymptotics and Exact Calculations.” Journal of the Royal Statistical Society B 56 (3): 501–514.Google Scholar

  • Geweke, J. 2005. Contemporary Bayesian Econometrics and Statistics. New Jersey: John Wiley & Sons Ltd.Google Scholar

  • Gordon, S., and J. Maheu. 2008. “Learning, Forecasting and Structural Breaks.” Journal of Applied Econometrics 23 (5): 553–583.Web of ScienceCrossrefGoogle Scholar

  • Jacquiera, E., N. G. Polson, and P. E. Rossi. 1994. “Bayesian Analysis of Stochastic Volatility Models.” Journal of Business and Economic Statistics 12 (4): 371–389.Google Scholar

  • Jacquiera, E., N. G. Polson, and P. E. Rossi. 2004. “Bayesian Analysis of Stochastic Volatility Models With Fat-Tails and Correlated Errors.” Journal of Econometrics 122 (1): 185–212.CrossrefGoogle Scholar

  • Kass, R. E., and A. E. Raftery. 1995. “Bayes Factors.” Journal of the American Statistical Association 90: 773–795.CrossrefGoogle Scholar

  • Kim, C. J., and C. R. Nelson. 1999a. State Space Models with Regime Switching Classical and Gibbs Sampling Approaches with Applications. Cambridge, MA: MIT Press.Google Scholar

  • Kim, C. J., and C. R. Nelson. 1999b. “Has the U.S. Economy Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of Business Cycle.” Review of Economics and Statistics 81 (4): 608–616.CrossrefGoogle Scholar

  • Kim, C. J., C. R. Nelson, and J. Piger. 2004. “The Less Volatile U.S. Economy: A Bayesian Investigation of Timing, Breadth, and Potential Explanations.” Journal of Business and Economic Statistics 22 (1): 80–93.Google Scholar

  • Kim, S., N. Shephard, and S. Chib. 1998. “Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models.” Review of Economic Studies 65 (3): 361–393.CrossrefGoogle Scholar

  • Koop, G. 2003. Bayesian Econometrics. England: John Wiley & Sons Ltd.Google Scholar

  • Koopman, S. J., and E. H. Uspensky. 2002. “The Stochastic Volatility in Mean Model: Empirical Evidence from International Stock Markets.” Journal of Applied Econometrics 17 (6): 667–689.CrossrefGoogle Scholar

  • Lindsten, F., M. I. Jordan, and T. B. Schön. 2012. “Ancestor Sampling for Particle Gibbs.” Advances in Neural Information Processing Systems (NIPS) 25: 2600–2608.Google Scholar

  • Lindsten, F., M. I. Jordan, and T. B. Schön. 2014. “Particle Gibbs with Ancestor Sampling.” Journal of Machine Learning Research 15: 2145–2184.Google Scholar

  • Lindsten, F., and T. B. Schön. 2013. “Backward Simulation Methods for Monte Carlo Statistical Inference.” Foundations and Trends in Machine Learning 6 (1): 1–14.Google Scholar

  • Liu, C., and J. Maheu. 2008. “Are There Structural Breaks in Realized Volatility?” Journal of Financial Econometrics 6 (3): 326–360.CrossrefWeb of ScienceGoogle Scholar

  • Malik, S., and M. K. Pitt. 2011. “Modelling Stochastic Volatility with Leverage and Jumps: A Simulated Maximum Likelihood Approach Via Particle Filtering.” Working paper, University of Warwick.Google Scholar

  • Marcellino, M., J. H. Stock, and M. W. Watson. 2005. “A Comparison of Direct and Iterated AR Methods for Forecasting Macroeconomic Series h-Steps Ahead.” Journal of Econometrics 134 (2): 425–449.Google Scholar

  • Nakajima, J., and Y. Omori. 2012. “Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student’s t-Distribution.” Computational Statistics and Data Analysis 56 (11): 3690–3704.Web of ScienceCrossrefGoogle Scholar

  • Omori, Y., S. Chib, N. Shephard, and J. Nakajima. 2007. “Stochastic Volatility with Leverage: Fast and Efficient Likelihood Inference.” Journal of Econometrics 135 (1–2): 499–526.Web of ScienceGoogle Scholar

  • Primiceri, G. E. 2005. “Time Varying Structural Vector Autoregressions and Monetary Policy.” Review of Economic Studies 72 (3): 821–852.CrossrefGoogle Scholar

  • Raggi, D., and S. Bordignon. 2012. “Long Memory and Nonlinearities in Realized Volatility: A Markov Switching Approach.” Computational Statistics and Data Analysis 56 (11): 3730–3742.CrossrefWeb of ScienceGoogle Scholar

  • Sims, C. A., D. F. Waggoner, and T. Zha. 2008. “Methods for Inference in Large Multiple-Equation Markov-Switching Models.” Journal of Econometrics 146 (2): 255–274.Web of ScienceCrossrefGoogle Scholar

  • Spiegelhalter, D., N. Best, B. Carlin, and A. van der Linde. 2002. “Bayesian Measures of Model Complexity and Fit (with comments).” Journal of the Royal Statistical Society B 64 (4): 583–639.CrossrefGoogle Scholar

  • Stock, J. H., and M. W. Watson. 2007. “Why Has U.S. Inflation Become Harder to Forecast?” Journal of Money, Credit, and Banking 39 (1): 3–34.CrossrefGoogle Scholar

  • Whiteley, N., C. Andrieu, and A. Doucet. 2010. “Efficient Bayesian Inference for Switching State-Space Models using Particle Markov chain Monte Carlo methods.” Bristol Statistics Research Report 10:04.Google Scholar

  • Zellner, A. 1986. “Bayesian Estimation and Prediction Using Asymmetric Loss Functions.” Journal of the American Statistical Association 81: 446–451.CrossrefGoogle Scholar

About the article

Corresponding author: Nima Nonejad, Aarhus University and Creates – Department of Economics and Business, Fuglesangs Alle 4, Aarhus 8210, Aarhus V, Denmark, e-mail:


Published Online: 2015-04-21

Published in Print: 2015-12-01


Citation Information: Studies in Nonlinear Dynamics & Econometrics, Volume 19, Issue 5, Pages 561–584, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2014-0043.

Export Citation

©2015 by De Gruyter.Get Permission

Supplementary Article Materials

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Joshua C.C. Chan
Journal of Business & Economic Statistics, 2018, Page 1

Comments (0)

Please log in or register to comment.
Log in