Type: Package
Title: Comprehensive Cointegration Tests with Fourier and Panel Methods
Version: 1.0.0
Description: A unified toolkit for cointegration testing including Fourier-based cointegration tests (FADL, FEG, FEG2, Tsong) that accommodate smooth structural breaks via flexible Fourier terms, and panel CADF cointegration tests with structural breaks using the Common Correlated Effects (CCE) estimator following Banerjee, Arcabic and Lee (2017) <doi:10.1016/j.econmod.2017.03.004>, Tsong, Lee, Tsai and Hu (2016) <doi:10.1007/s00181-015-1028-6>, and Banerjee and Carrion-i-Silvestre (2025) <doi:10.1080/07350015.2024.2327844>.
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.3.2
Depends: R (≥ 3.5.0)
Imports: stats
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2026-03-24 11:13:25 UTC; acad_
Author: Muhammad Abdullah Alkhalaf ORCID iD [aut, cre, cph]
Maintainer: Muhammad Abdullah Alkhalaf <muhammedalkhalaf@gmail.com>
Repository: CRAN
Date/Publication: 2026-03-27 11:10:08 UTC

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. 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. 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)

Print Method for fcoint Objects

Description

Prints a formatted summary of Fourier cointegration test results.

Usage

## S3 method for class 'fcoint'
print(x, ...)

Arguments

x

An object of class "fcoint".

...

Further arguments passed to or from other methods (unused).

Value

Invisibly returns x.

Examples

set.seed(1)
n <- 60
x <- cumsum(rnorm(n))
y <- 0.5 * x + rnorm(n)
res <- fcoint(y, x, test = "fadl", max_freq = 2)
print(res)

Print Method for xtcadfcoint Objects

Description

Prints a formatted summary of an "xtcadfcoint" result.

Usage

## S3 method for class 'xtcadfcoint'
print(x, ...)

Arguments

x

An object of class "xtcadfcoint".

...

Additional arguments (ignored).

Value

Invisibly returns x.

Summary Method for xtcadfcoint Objects

Description

Prints a summary of an "xtcadfcoint" result.

Usage

## S3 method for class 'xtcadfcoint'
summary(object, ...)

Arguments

object

An object of class "xtcadfcoint".

...

Additional arguments (ignored).

Value

Invisibly returns object.

Panel CADF Cointegration Test with Structural Breaks

Description

Tests the null hypothesis of no cointegration in panel data using the cross-sectionally augmented Dickey-Fuller (CADF) approach of Banerjee and Carrion-i-Silvestre (2025). Accounts for cross-sectional dependence via the Common Correlated Effects (CCE) estimator and allows for structural breaks.

Usage

xtcadfcoint(formula, data, index, model = 1, breaks = 0,
            trimming = 0.15, maxlags = 4, lagselect = "bic",
            nfactors = 1, brk_slope = FALSE, brk_loadings = FALSE,
            cce = TRUE, simulate = 0, level = 95)

Arguments

formula

A formula of the form y ~ x1 + x2 + ....

data

A data frame in long format.

index

Character vector of length 2: c("id_var", "time_var").

model

Integer (0-5) specifying the deterministic component.

breaks

Integer (0, 1, or 2). Number of structural breaks.

trimming

Numeric. Trimming fraction for break date search. Default 0.15.

maxlags

Maximum lag order for ADF augmentation. Default 4.

lagselect

Lag selection: "bic", "aic", "maic", "mbic", or "fixed".

nfactors

Integer. Number of common factors for CCE. Default 1.

brk_slope

Logical. Allow breaks in cointegrating vector slopes.

brk_loadings

Logical. Allow breaks in factor loadings.

cce

Logical. Apply CCE augmentation. Default TRUE.

simulate

Integer. Bootstrap replications for critical values (0 = skip).

level

Confidence level in percent. Default 95.

Value

An object of class "xtcadfcoint" containing panel CIPS statistics, individual CADF statistics, estimated break dates, and coefficient estimates.

References

Banerjee, A. and Carrion-i-Silvestre, J.L. (2024). Panel Data Cointegration Testing with Structural Instabilities. Journal of Business & Economic Statistics, 43, 122–133. doi:10.1080/07350015.2024.2327844

Examples


set.seed(42)
n <- 5; tt <- 30
uid  <- rep(1:n, each = tt)
tval <- rep(1:tt, times = n)
x_it <- cumsum(rnorm(n * tt))
y    <- x_it + rnorm(n * tt, sd = 0.5)
dat  <- data.frame(id = uid, time = tval, y = y, x = x_it)
res  <- xtcadfcoint(y ~ x, data = dat, index = c("id", "time"), model = 1)
print(res)