IDEAS home Printed from https://ideas.repec.org/p/een/camaaa/2015-07.html
   My bibliography  Save this paper

The Stochastic Volatility in Mean Model with Time-Varying Parameters: An Application to Inflation Modeling

Author

Listed:
  • Joshua C.C. Chan

Abstract

This paper generalizes the popular stochastic volatility in mean model of Koopman and Hol Uspensky (2002) to allow for time-varying parameters in the conditional mean. The estimation of this extension is nontrival since the volatility appears in both the conditional mean and the conditional variance, and its coefficient in the former is time-varying. We develop an efficient Markov chain Monte Carlo algorithm based on band and sparse matrix algorithms instead of the Kalman filter to estimate this more general variant. We illustrate the methodology with an application that involves US, UK and Germany inflation. The estimation results show substantial time-variation in the coefficient associated with the volatility, high-lighting the empirical relevance of the proposed extension. Moreover, in a pseudo out-of-sample forecasting exercise, the proposed variant also forecasts better than various standard benchmarks.

Suggested Citation

  • Joshua C.C. Chan, 2015. "The Stochastic Volatility in Mean Model with Time-Varying Parameters: An Application to Inflation Modeling," CAMA Working Papers 2015-07, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2015-07
    as

    Download full text from publisher

    File URL: https://cama.crawford.anu.edu.au/sites/default/files/publication/cama_crawford_anu_edu_au/2015-03/7_2015_chan.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Berument, Hakan & Yalcin, Yeliz & Yildirim, Julide, 2009. "The effect of inflation uncertainty on inflation: Stochastic volatility in mean model within a dynamic framework," Economic Modelling, Elsevier, vol. 26(6), pages 1201-1207, November.
    2. Haroon Mumtaz & Francesco Zanetti, 2013. "The Impact of the Volatility of Monetary Policy Shocks," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(4), pages 535-558, June.
    3. McCausland, William J. & Miller, Shirley & Pelletier, Denis, 2011. "Simulation smoothing for state-space models: A computational efficiency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 199-212, January.
    4. Joshua C.C. Chan & Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2012. "Time Varying Dimension Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 358-367, January.
    5. Eric Eisenstat & Rodney W. Strachan, 2016. "Modelling Inflation Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(5), pages 805-820, August.
    6. Canova, Fabio, 1993. "Modelling and forecasting exchange rates with a Bayesian time-varying coefficient model," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 233-261.
    7. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    9. Antonello D'Agostino & Luca Gambetti & Domenico Giannone, 2013. "Macroeconomic forecasting and structural change," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(1), pages 82-101, January.
    10. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    11. Håvard Rue, 2001. "Fast sampling of Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 325-338.
    12. Joshua C. C. Chan & Gary Koop & Simon M. Potter, 2013. "A New Model of Trend Inflation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 94-106, January.
    13. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2010. "Dynamic Probabilities of Restrictions in State Space Models: An Application to the Phillips Curve," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 370-379.
    14. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
    15. Holland, A Steven, 1995. "Inflation and Uncertainty: Tests for Temporal Ordering," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(3), pages 827-837, August.
    16. John Geweke & Gianni Amisano, 2011. "Hierarchical Markov normal mixture models with applications to financial asset returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 1-29, January/F.
    17. Todd E. Clark, 2011. "Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 327-341, July.
    18. McCausland, William J., 2012. "The HESSIAN method: Highly efficient simulation smoothing, in a nutshell," Journal of Econometrics, Elsevier, vol. 168(2), pages 189-206.
    19. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    20. James H. Stock & Mark W. Watson, 2010. "Modeling inflation after the crisis," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 173-220.
    21. Todd E. Clark & Francesco Ravazzolo, 2015. "Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 551-575, June.
    22. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    23. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    24. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    25. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    26. Joshua C.C. Chan & Rodney Strachan, 2014. "The Zero Lower Bound: Implications for Modelling the Interest Rate," Working Paper series 42_14, Rimini Centre for Economic Analysis.
    27. Canova, Fabio, 2007. "G-7 Inflation Forecasts: Random Walk, Phillips Curve Or What Else?," Macroeconomic Dynamics, Cambridge University Press, vol. 11(1), pages 1-30, February.
    28. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    29. Cukierman, Alex & Meltzer, Allan H, 1986. "A Theory of Ambiguity, Credibility, and Inflation under Discretion and Asymmetric Information," Econometrica, Econometric Society, vol. 54(5), pages 1099-1128, September.
    30. Ball, Laurence, 1992. "Why does high inflation raise inflation uncertainty?," Journal of Monetary Economics, Elsevier, vol. 29(3), pages 371-388, June.
    31. Timothy Cogley & Giorgio E. Primiceri & Thomas J. Sargent, 2010. "Inflation-Gap Persistence in the US," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 43-69, January.
    32. Barnabé Djegnéné & William J. McCausland, 2015. "The HESSIAN Method for Models with Leverage-like Effects," Journal of Financial Econometrics, Oxford University Press, vol. 13(3), pages 722-755.
    33. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    34. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    35. Friedman, Milton, 1977. "Nobel Lecture: Inflation and Unemployment," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 451-472, June.
    36. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    37. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    38. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joshua C.C. Chan & Rodney W. Strachan, 2023. "Bayesian State Space Models In Macroeconometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 58-75, February.
    2. Joshua C. C. Chan, 2018. "Specification tests for time-varying parameter models with stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 807-823, September.
    3. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    4. Terence D. Agbeyegbe, 2023. "The Link Between Output Growth and Output Growth Volatility: Barbados," Annals of Data Science, Springer, vol. 10(3), pages 787-804, June.
    5. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    6. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong & Zhuang, Xin-Tian, 2018. "Modeling volatility dynamics using non-Gaussian stochastic volatility model based on band matrix routine," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 193-201.
    7. Joshua C.C. Chan & Angelia L. Grant, 2014. "Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion," CAMA Working Papers 2014-51, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    8. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    9. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    10. Marta Banbura & Andries van Vlodrop, 2018. "Forecasting with Bayesian Vector Autoregressions with Time Variation in the Mean," Tinbergen Institute Discussion Papers 18-025/IV, Tinbergen Institute.
    11. Joshua C. C. Chan, 2019. "Large Bayesian vector autoregressions," CAMA Working Papers 2019-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    12. Benjamin K. Johannsen & Elmar Mertens, 2021. "A Time‐Series Model of Interest Rates with the Effective Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(5), pages 1005-1046, August.
    13. Todd E. Clark & Michael W. McCracken & Elmar Mertens, 2020. "Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 17-33, March.
    14. Claudiu Tiberiu Albulescu & Cornel Oros, 2020. "Inflation, uncertainty, and labour market conditions in the US," Applied Economics, Taylor & Francis Journals, vol. 52(52), pages 5770-5782, November.
    15. Legrand, Romain, 2018. "Time-Varying Vector Autoregressions: Efficient Estimation, Random Inertia and Random Mean," MPRA Paper 88925, University Library of Munich, Germany.
    16. Nima Nonejad, 2021. "An Overview Of Dynamic Model Averaging Techniques In Time‐Series Econometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 566-614, April.
    17. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    18. Carriero, Andrea & Clark, Todd E. & Marcellino, Massimiliano & Mertens, Elmar, 2023. "Shadow-rate VARs," Discussion Papers 14/2023, Deutsche Bundesbank.
    19. Fuest, Angela & Schmidt, Torsten, 2017. "Inflation expectation uncertainty, inflation and the output gap," Ruhr Economic Papers 673, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    20. Niko Hauzenberger, 2020. "Flexible Mixture Priors for Large Time-varying Parameter Models," Papers 2006.10088, arXiv.org, revised Nov 2020.

    More about this item

    Keywords

    nonlinear; state space; inflation forecasting; inflation uncertainty;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:een:camaaa:2015-07. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Cama Admin (email available below). General contact details of provider: https://edirc.repec.org/data/asanuau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.