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Specification tests for time-varying parameter models with stochastic volatility

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  • Joshua C.C. Chan

Abstract

We propose an easy technique to test for time-variation in coefficients and volatilities. Specifically, by using a noncentered parameterization for state space models, we develop a method to directly calculate the relevant Bayes factor using the Savage-Dickey density ratio—thus avoiding the computation of the marginal likelihood altogether. The proposed methodology is illustrated via two empirical applications. In the first application we test for time-variation in the volatility of inflation in the G7 countries. The second application investigates if there is substantial time-variation in the NAIRU in the US.

Suggested Citation

  • Joshua C.C. Chan, 2015. "Specification tests for time-varying parameter models with stochastic volatility," CAMA Working Papers 2015-42, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2015-42
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    Cited by:

    1. Bańbura, Marta & Leiva-León, Danilo & Menz, Jan-Oliver, 2021. "Do inflation expectations improve model-based inflation forecasts?," Discussion Papers 48/2021, Deutsche Bundesbank.
    2. Ana Beatriz Galvão & James Mitchell, 2019. "Measuring Data Uncertainty: An Application using the Bank of England's "Fan Charts" for Historical GDP Growth," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2019-08, Economic Statistics Centre of Excellence (ESCoE).
    3. Manuel M. F. Martins & Fabio Verona, 2021. "Inflation Dynamics and Forecast: Frequency Matters," CEF.UP Working Papers 2101, Universidade do Porto, Faculdade de Economia do Porto.
    4. Afees A. Salisu & Idris Adediran, 2018. "Testing for time-varying stochastic volatility in Bitcoin returns," Working Papers 060, Centre for Econometric and Allied Research, University of Ibadan.
    5. Raffaella Giacomini & Katja Smetanina & Jason Lu, 2024. "Perceived shocks and impulse responses," IFS Working Papers WCWP21/24, Institute for Fiscal Studies.
    6. Bańbura, Marta & Bobeica, Elena, 2023. "Does the Phillips curve help to forecast euro area inflation?," International Journal of Forecasting, Elsevier, vol. 39(1), pages 364-390.
    7. Raffaella Giacomini & Jason Lu & Katja Smetanina, 2024. "Perceived shocks and impulse responses," CeMMAP working papers 21/24, Institute for Fiscal Studies.
    8. Julien Champagne & Guillaume Poulin‐Bellisle & Rodrigo Sekkel, 2020. "Introducing the Bank of Canada staff economic projections database," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 114-129, January.
    9. Mónica Correa-López & Matías Pacce & Kathi Schlepper, 2019. "Exploring trend inFLation dynamics in Euro Area countries," Working Papers 1909, Banco de España.
    10. Yu Bai & Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2022. "Macroeconomic forecasting in a multi‐country context," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1230-1255, September.
    11. Helmut Lutkepohl & Fei Shang & Luis Uzeda & Tomasz Wo'zniak, 2024. "Partial Identification of Structural Vector Autoregressions with Non-Centred Stochastic Volatility," Papers 2404.11057, arXiv.org, revised Oct 2025.
    12. Michal Franta & Ivan Sutoris, 2020. "Dynamics of Czech Inflation: The Role of the Trend and the Cycle," Working Papers 2020/1, Czech National Bank, Research and Statistics Department.
    13. Alex, Dony, 2021. "Anchoring of inflation expectations in large emerging economies," The Journal of Economic Asymmetries, Elsevier, vol. 23(C).
    14. Afees A. Salisu & Ahamuefula Ephraim Ogbonna, 2018. "Does time-variation matter in the stochastic volatility components for G7 stock returns," Working Papers 062, Centre for Econometric and Allied Research, University of Ibadan.
    15. Marek Jarociński & Michele Lenza, 2018. "An Inflation‐Predicting Measure of the Output Gap in the Euro Area," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(6), pages 1189-1224, September.
    16. James Mitchell & Donald Robertson & Stephen Wright, 2019. "R2 Bounds for Predictive Models: What Univariate Properties Tell us About Multivariate Predictability," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 681-695, October.
    17. 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.
    18. Amaze Lusompa & Sai Sattiraju, 2023. "Will High Underlying Inflation Persist?," Economic Bulletin, Federal Reserve Bank of Kansas City, pages 1-4, May.
    19. Chi-Young Choi & Alexander Chudik & Aaron Smallwood, 2024. "Time-varying Persistence of House Price Growth: The Role of Expectations and Credit Supply," Globalization Institute Working Papers 426, Federal Reserve Bank of Dallas.
    20. Helmut Lütkepohl & Fei Shang & Luis Uzeda & Tomasz Woźniak, 2024. "Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference," Discussion Papers of DIW Berlin 2081, DIW Berlin, German Institute for Economic Research.
    21. Ramis Khabibullin, 2019. "What measures of real economic activity slack are helpful for forecasting Russian inflation?," Bank of Russia Working Paper Series wps50, Bank of Russia.
    22. Cross, Jamie L. & Hou, Chenghan & Trinh, Kelly, 2021. "Returns, volatility and the cryptocurrency bubble of 2017–18," Economic Modelling, Elsevier, vol. 104(C).
    23. Fu, Bowen, 2020. "Is the slope of the Phillips curve time-varying? Evidence from unobserved components models," Economic Modelling, Elsevier, vol. 88(C), pages 320-340.
    24. Balatti, Mirco, 2020. "Inflation volatility in small and large advanced open economies," Working Paper Series 2448, European Central Bank.
    25. Bańbura, Marta & Brenna, Federica & Paredes, Joan & Ravazzolo, Francesco, 2021. "Combining Bayesian VARs with survey density forecasts: does it pay off?," Working Paper Series 2543, European Central Bank.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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