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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.

Suggested Citation

  • Yohei Yamamoto & Pierre Perron, 2012. "Estimating and Testing Multiple Structural Changes in Linear Models Using Band Spectral Regressions," Global COE Hi-Stat Discussion Paper Series gd12-250, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd12-250
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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd12-250.pdf
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    References listed on IDEAS

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    Cited by:

    1. Seong Yeon Chang & Pierre Perron, 2013. "A Comparison of Alternative Methods to Construct Confidence Intervals for the Estimate of a Break Date in Linear Regression Models," Boston University - Department of Economics - Working Papers Series wp2015-010, Boston University - Department of Economics, revised 11 Oct 2015.
    2. Seongyeon Chang & Pierre Perron, 2013. "A Comparison of Alternative Methods to Construct to Confidence Intervals for the Estimate of a Break Date in Linear Regression Models," Boston University - Department of Economics - Working Papers Series 2013-023, Boston University - Department of Economics.
    3. 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.
    4. Busch, Marie & Sibbertsen, Philipp, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Hannover Economic Papers (HEP) dp-628, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    5. repec:eee:asieco:v:50:y:2017:i:c:p:46-61 is not listed on IDEAS

    More about this item

    Keywords

    multiple structural changes; band spectral regression; low frequency contaminations; hours-productivity; business-cycle;

    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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