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FCOINT: Stata module to perform Fourier cointegration tests for time series with smooth structural breaks

Author

Listed:
  • Merwan Roudane

Programming Language

Abstract

fcoint implements four Fourier-based cointegration tests for time-series data. The tests use low-frequency Fourier (trigonometric) components to approximate smooth structural breaks of unknown form in the deterministic trend, without needing to estimate the number, timing, or form of breaks. This is important because conventional cointegration tests (Engle-Granger, Johansen, ADL) can fail to detect cointegration when the equilibrium relationship has undergone smooth structural shifts — such as gradual policy changes, evolving market structures, or slow institutional reforms. The key idea is that a Fourier expansion sin(2{c pi}kt/T) + cos(2{c pi}kt/T) can approximate virtually any smooth deterministic function, including functions with multiple breaks and nonlinear shifts (Gallant, 1981). This avoids the pitfalls of dummy-variable approaches, which require pre-specifying break dates and forms.

Suggested Citation

  • Merwan Roudane, 2026. "FCOINT: Stata module to perform Fourier cointegration tests for time series with smooth structural breaks," Statistical Software Components S459628, Boston College Department of Economics.
    • Handle: RePEc:boc:bocode:s459628
    Note: This module should be installed from within Stata by typing "ssc install fcoint". The module is made available under terms of the GPL v3 (https://www.gnu.org/licenses/gpl-3.0.txt). Windows users should not attempt to download these files with a web browser.
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    File URL: http://fmwww.bc.edu/repec/bocode/f/fcoint.ado
    File Function: program code
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    File URL: http://fmwww.bc.edu/repec/bocode/f/fcoint.sthlp
    File Function: help file
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_critvals.ado
    File Function: program code
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_fadl_cumul.ado
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_fadl_single.ado
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_fadl.ado
    File Function: program code
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_feg2.ado
    File Function: program code
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_tsong_ftest.ado
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_tsong.ado
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_fadl.ado
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_feg.ado
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_feg2.ado
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    File URL: http://fmwww.bc.edu/repec/bocode/_/_fcoint_tsong.ado
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