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Trend-cycle decomposition allowing for multiple smooth structural changes in the trend of US real GDP

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  • Enders, Walter
  • Li, Jing

Abstract

A key feature of Flexible Fourier Form (FFF) is that the essential characteristics of multiple structural changes can be captured using a small number of low frequency components from a Fourier approximation. We introduce a variant of the FFF into the trend function of US real GDP in order to allow for gradual effects of unknown numbers of structural changes occurring at unknown dates. We find that the hypothesis of no changes can be rejected, and the Fourier components are significant. Our new cycle matches the NBER chronology very well, especially for the Great Recession of 2009.

Suggested Citation

  • Enders, Walter & Li, Jing, 2015. "Trend-cycle decomposition allowing for multiple smooth structural changes in the trend of US real GDP," Journal of Macroeconomics, Elsevier, vol. 44(C), pages 71-81.
    • Handle: RePEc:eee:jmacro:v:44:y:2015:i:c:p:71-81
    DOI: 10.1016/j.jmacro.2015.02.002
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    2. Xu, Chang & Katchova, Ani L., 2019. "Predicting Soybean Yield with NDVI Using a Flexible Fourier Transform Model," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 51(3), pages 402-416, August.
    3. Magdalena Osińska & Tadeusz Kufel & Marcin Błażejowski & Paweł Kufel, 2020. "Modeling mechanism of economic growth using threshold autoregression models," Empirical Economics, Springer, vol. 58(3), pages 1381-1430, March.
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    5. Banerjee, Piyali & Arčabić, Vladimir & Lee, Hyejin, 2017. "Fourier ADL cointegration test to approximate smooth breaks with new evidence from Crude Oil Market," Economic Modelling, Elsevier, vol. 67(C), pages 114-124.
    6. Gyurkovics, Éva & Takács, Tibor, 2022. "Robust energy-to-peak filter design for a class of unstable polytopic systems with a macroeconomic application," Applied Mathematics and Computation, Elsevier, vol. 420(C).

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    More about this item

    Keywords

    Trend-cycle decomposition; Flexible Fourier form; Smooth structural changes;
    All these keywords.

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • 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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