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Stochastic Volatility Models with ARMA Innovations: An Application to G7 Inflation Forecasts

Author

Listed:
  • Bo Zhang
  • Joshua C.C. Chan
  • Jamie L. Cross

Abstract

We introduce a new class of stochastic volatility models with autoregressive moving average (ARMA) innovations. The conditional mean process has a flexible form that can accommodate both a state space representation and a conventional dynamic regression. The ARMA component introduces serial dependence which renders standard Kalman filter techniques not directly applicable. To overcome this hurdle we develop an efficient posterior simulator that builds on recently developed precision based algorithms. We assess the usefulness of these new models in an inflation forecasting exercise across all G7 economies. We find that the new models generally provide competitive point and density forecasts compared to standard benchmarks, and are especially useful for Canada, France, Italy and the US.

Suggested Citation

  • Bo Zhang & Joshua C.C. Chan & Jamie L. Cross, 2018. "Stochastic Volatility Models with ARMA Innovations: An Application to G7 Inflation Forecasts," CAMA Working Papers 2018-32, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2018-32
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    Cited by:

    1. Matteo Mogliani & Anna Simoni, 2024. "Bayesian Bi-level Sparse Group Regressions for Macroeconomic Density Forecasting," Papers 2404.02671, arXiv.org, revised Nov 2024.
    2. Na Guo & Bo Zhang & Jamie L. Cross, 2022. "Time‐varying trend models for forecasting inflation in Australia," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 316-330, March.
    3. Marco Del Negro & Michele Lenza & Giorgio E. Primiceri & Andrea Tambalotti, 2020. "What's Up with the Phillips Curve?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 51(1 (Spring), pages 301-373.
    4. Chan, Joshua C.C. & Poon, Aubrey & Zhu, Dan, 2023. "High-dimensional conditionally Gaussian state space models with missing data," Journal of Econometrics, Elsevier, vol. 236(1).
    5. Boriss Siliverstovs, 2020. "Assessing nowcast accuracy of US GDP growth in real time: the role of booms and busts," Empirical Economics, Springer, vol. 58(1), pages 7-27, January.
    6. Arango-Castillo, Lenin & Orraca, María José & Molina, G. Stefano, 2023. "The global component of headline and core inflation in emerging market economies and its ability to improve forecasting performance," Economic Modelling, Elsevier, vol. 120(C).
    7. Zhang, Bo & Nguyen, Bao H., 2020. "Real-time forecasting of the Australian macroeconomy using Bayesian VARs," Working Papers 2020-12, University of Tasmania, Tasmanian School of Business and Economics.
    8. Chenghan Hou & Bao Nguyen & Bo Zhang, 2023. "Real‐time forecasting of the Australian macroeconomy using flexible Bayesian VARs," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 418-451, March.
    9. Gergely Ganics & Lluc Puig Codina, 2025. "Simple Tests for the Correct Specification of Conditional Predictive Densities," Working Papers 2535, Banco de España.
    10. Jihyun Park & Andrey Sarantsev, 2024. "The VIX as Stochastic Volatility for Corporate Bonds," Papers 2410.22498, arXiv.org, revised Jan 2025.
    11. Jamie L. Cross & Chenghan Hou & Gary Koop, 2021. "Macroeconomic Forecasting with Large Stochastic Volatility in Mean VARs," Working Papers No 04/2021, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    12. Yuntong Liu & Yu Wei & Yi Liu & Wenjuan Li, 2020. "Forecasting Oil Price by Hierarchical Shrinkage in Dynamic Parameter Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-12, December.

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    Keywords

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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