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State Space Model with Mixtures of Normals: Specifications and Applications to International Data

Author

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  • Tatsuma Wada

    () (Department of Economics, Boston University\par)

  • Pierre Perron

    () (Department of Economics, Boston University)

Abstract

This paper first generalizes the trend-cycle decomposition framework of Perron and Wada (2005) based on an unobserved components model with innovations having a mixture of Normal distribution, which is able to handle sudden level and slope changes to the trend function as well as outliers. We investigate how important are the differences in the implied trend and cycle compared to the popular decomposition based on the Hodrick and Prescott (HP) (1997) filter. Our results show important qualitative and quantitative differences in the implied cycles for both real GDP and consumption series for the G7 countries. Most of the differences can be ascribed to the fact that the HP filter does not handle well slope changes, level shifts and outliers, while our method does so. Third, we assess how such different cycles affect some so-called “stylized facts†about the relative variability of consumption and output across countries. Our results show again important differences. In particular, the cross-country consumption correlations are generally higher than the output correlations, except for the period from 1975 to 1985, provided Canada is excluded. Our results therefore provide a partial solution to this puzzle. The evidence is particularly strong for the most recent period.

Suggested Citation

  • Tatsuma Wada & Pierre Perron, 2006. "State Space Model with Mixtures of Normals: Specifications and Applications to International Data," Boston University - Department of Economics - Working Papers Series WP2006-029, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2006-029
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Perron, Pierre & Wada, Tatsuma, 2009. "Let's take a break: Trends and cycles in US real GDP," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 749-765, September.
    2. Seong Yeon Chang & Pierre Perron, 2016. "Inference on a Structural Break in Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, pages 555-574.
    3. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, pages 138-156.
    4. Gabriel Rodriguez & Roxana Tramontana, 2014. " An Application of a Short Memory Model With Random Level Shifts to the Volatility of Latin American Stock Market Returns," Documentos de Trabajo / Working Papers 2014-385, Departamento de Economía - Pontificia Universidad Católica del Perú.
    5. Yang K. Lu & Pierre Perron, 2008. "Modeling and Forecasting Stock Return Volatility Using a Random Level Shift Model," Boston University - Department of Economics - Working Papers Series wp2008-012, Boston University - Department of Economics.
    6. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    7. Mitra, Sinchan & Sinclair, Tara M., 2012. "Output Fluctuations In The G-7: An Unobserved Components Approach," Macroeconomic Dynamics, Cambridge University Press, pages 396-422.
    8. Karim Barhoumi & Reda Cherif & Nooman Rebei, 2016. "Stochastic Trends, Debt Sustainability and Fiscal Policy," IMF Working Papers 16/59, International Monetary Fund.
    9. Yohei Yamamoto & Pierre Perron, 2013. "Estimating and testing multiple structural changes in linear models using band spectral regressions," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 400-429, October.
    10. Xu, Jiawen & Perron, Pierre, 2014. "Forecasting return volatility: Level shifts with varying jump probability and mean reversion," International Journal of Forecasting, Elsevier, vol. 30(3), pages 449-463.
    11. Luis Filipe Martins & Pierre Perron, 2016. "Improved Tests for Forecast Comparisons in the Presence of Instabilities," Journal of Time Series Analysis, Wiley Blackwell, pages 650-659.
    12. Ángel Guillén & Gabriel Rodríguez, 2014. "Trend-cycle decomposition for Peruvian GDP: application of an alternative method," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), pages 1-44.
    13. Gabriel Rodríguez, 2015. "Modeling Latin-American Stock Markets Volatility: Varying Probabilities and Mean Reversion in a Random Level Shifts Model," Documentos de Trabajo / Working Papers 2015-403, Departamento de Economía - Pontificia Universidad Católica del Perú.
    14. Pierre Perron & Rasmus T. Varneskov, 2011. "Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns," Boston University - Department of Economics - Working Papers Series WP2011-050, Boston University - Department of Economics.
    15. Ángel Guillén & Gabriel Rodríguez, 2014. "Trend-cycle decomposition for Peruvian GDP: application of an alternative method," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), pages 1-44.

    More about this item

    Keywords

    Trend-Cycle Decomposition; Unobserved Components Model; International Business Cycle; Non Gaussian Filter.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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