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Bayesian Analysis of Time-Varying Quantiles Using a Smoothing Spline

  • Yuta Kurose

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

A smoothing spline is considered to propose a novel model for the time-varying quantile of the univariate time series using a state space approach. A correlation is further incorporated between the dependent variable and its one-step-ahead quantile. Using a Bayesian approach, an efficient Markov chain Monte Carlo algorithm is described where we use the multi-move sampler, which generates simultaneously latent time-varying quantiles. Numerical examples are provided to show its high sampling efficiency in comparison with the simple algorithm that generates one latent quantile at a time given other latent quantiles. Furthermore, using Japanese inflation rate data, an empirical analysis is provided with the model comparison.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-845.

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Length: 29 pages
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:tky:fseres:2012cf845
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  1. repec:cup:cbooks:9780521608275 is not listed on IDEAS
  2. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  3. Chan, Nancy Y. C. & Chen, Cathy W.S. & Gerlach, Richard, 2009. "Bayesian time-varying quantile forecasting for Value-at-Risk in financial markets," Working Papers 01/2009, University of Sydney Business School, Discipline of Business Analytics.
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  9. DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics 0660, Faculty of Economics, University of Cambridge.
  10. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, March.
  11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  12. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
  13. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
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