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Historical Decompositions for Nonlinear Vector Autoregression Models

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  • Benjamin Wong

Abstract

The historical decomposition is standard within the vector autogression (VAR) toolkit. It provides an interpretation of historical fluctuations in the modelled time series through the lens of the identified structural shocks. The proliferation of nonlinear VAR models naturally leads to extending the historical decomposition into nonlinear settings. This article discusses how to calculate an exact historical decomposition for a large class of popular nonlinear VAR models. In particular, the standard historical decomposition one obtains from a linear VAR is nested within the nonlinear case. The approach discussed in this article is sufficiently general to be relevant for many popular variants of nonlinear VAR models.

Suggested Citation

  • Benjamin Wong, 2017. "Historical Decompositions for Nonlinear Vector Autoregression Models," CAMA Working Papers 2017-62, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2017-62
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    File URL: https://crawford.anu.edu.au/sites/default/files/2025-01/62_2017_wong.pdf
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    2. Gabriel Rodriguez & Paul Castillo B. & Junior A. Ojeda Cunya, 2024. "Time-Varying Effects of External Shocks on Macroeconomic Fluctuations in Peru: An Empirical Application using TVP-VAR-SV Models," Open Economies Review, Springer, vol. 35(5), pages 1015-1050, November.
    3. Knotek, Edward S. & Zaman, Saeed, 2021. "Asymmetric responses of consumer spending to energy prices: A threshold VAR approach," Energy Economics, Elsevier, vol. 95(C).
    4. Alvarado, Mauricio & Rodríguez, Gabriel, 2025. "Time-varying effects of financial uncertainty shocks on macroeconomic fluctuations in Peru," Journal of International Money and Finance, Elsevier, vol. 152(C).
    5. Sohei Kaihatsu & Shogo Nakano & Hiroki Yamamoto, 2024. "Macroeconomic Impact of Shifts in Long-term Inflation Expectations," Bank of Japan Working Paper Series 24-E-18, Bank of Japan.
    6. Jiménez, Alvaro & Rodríguez, Gabriel & Ataurima Arellano, Miguel, 2023. "Time-varying impact of fiscal shocks over GDP growth in Peru: An empirical application using hybrid TVP-VAR-SV models," Structural Change and Economic Dynamics, Elsevier, vol. 64(C), pages 314-332.
    7. Atems, Bebonchu & Mette, Jehu & Lin, Guoyu & Madraki, Golshan, 2023. "Estimating and forecasting the impact of nonrenewable energy prices on US renewable energy consumption," Energy Policy, Elsevier, vol. 173(C).
    8. Meléndez, Alexander & Rodríguez, Gabriel, 2025. "Evolving impacts of fiscal policy on macroeconomic fluctuations in Peru," Economic Analysis and Policy, Elsevier, vol. 85(C), pages 1135-1158.
    9. Mauricio Alvarado & Gabriel Rodríguez, 2024. "Time-Varying Effects of Financial Uncertainty Shocks on Macroeconomic Fluctuations in Peru," Documentos de Trabajo / Working Papers 2024-531, Departamento de Economía - Pontificia Universidad Católica del Perú.
    10. Salha Ben Salem & Sonia Sayari & Moez Labidi, 2024. "Effect of Financial Frictions on Monetary Policy Conduct: A Comparative Analysis of DSGE Models with and without Financial Frictions," Economies, MDPI, vol. 12(3), pages 1-16, March.
    11. Koray YILDIRIM & Neşe ALGAN & Harun BAL, 2025. "The Dynamics of Output Gap Hysteresis in Türkiye," Journal of Research in Economics, Politics & Finance, Ersan ERSOY, vol. 10(1), pages 1-26.
    12. Alexander Meléndez Holguín & Gabriel Rodríguez, 2023. "Evolution over time of the effects of fiscal shocks in the peruvian economy: empirical application using TVP-VAR-SV models," Documentos de Trabajo / Working Papers 2023-516, Departamento de Economía - Pontificia Universidad Católica del Perú.
    13. Valentin Jouvanceau, 2023. "Consumer price rigidity in periods of low and high inflation: the case of Lithuania," Bank of Lithuania Discussion Paper Series 34, Bank of Lithuania.

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    JEL classification:

    • 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

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