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

Merwan Roudane ()

Statistical Software Components from Boston College Department of Economics

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.

Language: Stata
Requires: Stata version 14
Keywords: cointegration; Fourier; time series; structural breaks (search for similar items in EconPapers)
Date: 2026-03-07
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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http://fmwww.bc.edu/repec/bocode/f/fcoint.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/f/fcoint.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_critvals.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_fadl_cumul.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_fadl_single.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_fadl.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_feg2.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_tsong_ftest.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_cv_tsong.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_fadl.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_feg.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_feg2.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/_/_fcoint_tsong.ado program code (text/plain)

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