fcoint: Fourier Cointegration Tests for Time Series

In cointests: Comprehensive Cointegration Tests with Fourier and Panel Methods

Fourier Cointegration Tests for Time Series

Description

Implements four Fourier-based cointegration tests that accommodate smooth structural breaks via flexible Fourier terms: FADL, FEG, FEG2, and Tsong.

Usage

fcoint(y, x, test = c("fadl", "feg", "feg2", "tsong", "all"),
  model = c("constant", "trend"), max_freq = 5L, max_lag = 0L,
  criterion = c("aic", "bic"), dols_lags = 0L)

Arguments

y	Numeric vector. Dependent (left-hand side) time-series variable.
x	Numeric matrix or vector. Independent (right-hand side) variables.
test	Character. Which test to run: "fadl", "feg", "feg2", "tsong", or "all". Default is "fadl".
model	Character. Deterministic component: "constant" (default) or "trend".
max_freq	Integer. Maximum Fourier frequency to search over (1–5). Default is 5.
max_lag	Integer. Maximum lag order. 0 selects automatically via the information criterion. Default is 0.
criterion	Character. Information criterion for lag selection: "aic" (default) or "bic".
dols_lags	Integer. Leads and lags for the DOLS estimator used in the Tsong test. Default is 0 (automatic).

Details

The Fourier approach allows for smooth, nonlinear breaks in the deterministic components by augmenting standard cointegration regressions with one or more pairs of sine and cosine terms.

FADL (Banerjee, Arcabic & Lee, 2017): An ADL-type residual-based test. The optimal Fourier frequency k^* and lag order are chosen jointly by minimising the selected information criterion over a grid.

FEG and FEG2 (Banerjee & Lee): Engle-Granger style residual-based tests augmented with Fourier terms. FEG2 includes an additional R^2 correction.

Tsong et al. (2016): A DOLS-based cointegration test with Fourier terms. Reports both a CI statistic and an F-statistic for joint significance of Fourier terms.

Value

A list of class "fcoint" containing:

test

Character. Name(s) of the test(s) performed.

results

Named list of individual test results.

model

Character. Deterministic component used.

criterion

Character. Information criterion used.

nobs

Integer. Effective number of observations.

References

Banerjee, P., Arcabic, V., & Lee, H. (2017). Fourier ADL cointegration test to approximate smooth breaks with new evidence from crude oil market. Economic Modelling, 67, 114–124. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.econmod.2017.03.004")}

Tsong, C.-C., Lee, C.-F., Tsai, L.-J., & Hu, T.-C. (2016). The Fourier approximation and testing for the null of cointegration. Empirical Economics, 51(3), 1085–1113. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s00181-015-1028-6")}

Examples

set.seed(42)
n <- 80
x <- cumsum(rnorm(n))
y <- 0.5 * x + rnorm(n, sd = 0.3)
res <- fcoint(y, x, test = "fadl", max_freq = 3)
print(res)

cointests documentation built on March 27, 2026, 5:07 p.m.