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Estimating and testing multiple structural changes in linear models using band spectral regressions

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  • Yohei Yamamoto
  • Pierre Perron

Abstract

We provide methods for estimating and testing multiple structural changes occurring at unknown dates in linear models using band spectral regressions. We consider changes over time within some frequency bands, permitting the coefficients to be different across frequency bands. Using standard assumptions, we show that the limit distributions obtained are similar to those in the time domain counterpart. We show that when the coefficients change only within some frequency band, we have increased efficiency of the estimates and power of the tests. We also discuss a very useful application related to contexts in which the data is contaminated by some low frequency process (e.g., level shifts or trends) and that the researcher is interested in whether the original non-contaminated model is stable. All that is needed to obtain estimates of the break dates and tests for structural changes that are not affected by such low frequency contaminations is to truncate a low frequency band that shrinks to zero at rate log(T)/T. Simulations show that the tests have good sizes for a wide range of truncations so that the method is quite robust. We analyze the stability of the relation between hours worked and productivity. When applying structural change tests in the time domain we document strong evidence of instabilities. When excluding a few low frequencies, none of the structural change tests are significant. Hence, the results provide evidence to the effect that the relation between hours worked and productivity is stable over any spectral band that excludes the lowest frequencies, in particular it is stable over the business-cycle band.
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  • 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.
    • Handle: RePEc:wly:emjrnl:v:16:y:2013:i:3:p:400-429
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    File URL: http://hdl.handle.net/10.1111/ectj.2013.16.issue-3
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    2. Christensen, Bent Jesper & Varneskov, Rasmus Tangsgaard, 2017. "Medium band least squares estimation of fractional cointegration in the presence of low-frequency contamination," Journal of Econometrics, Elsevier, vol. 197(2), pages 218-244.
    3. Marie Busch & Philipp Sibbertsen, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Econometrics, MDPI, vol. 6(1), pages 1-21, March.
    4. Balakrishnan, Pulapre & Das, Mausumi & Parameswaran, M., 2017. "The internal dynamic of Indian economic growth," Journal of Asian Economics, Elsevier, vol. 50(C), pages 46-61.
    5. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    6. Aristeidis Samitas & Elias Kampouris & Zaghum Umar, 2022. "Financial contagion in real economy: The key role of policy uncertainty," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 1633-1682, April.
    7. Wada, Tatsuma, 2022. "Out-of-sample forecasting of foreign exchange rates: The band spectral regression and LASSO," Journal of International Money and Finance, Elsevier, vol. 128(C).

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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