Package 'cointests'

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)

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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)

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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.

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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.

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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)

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