Type:	Package
Title:	Multivariate ARDL Unit Root Test
Version:	1.0.2
Description:	Implements the multivariate autoregressive distributed lag (ARDL) unit root test proposed by Sam, McNown, Goh, and Goh (2024) <doi:10.1080/03796205.2024.2439101>. The test augments the standard ADF regression with lagged levels of a covariate to improve power when cointegration exists. Bootstrap critical values ensure correct size regardless of nuisance parameters. Provides automatic lag selection via AIC/BIC, diagnostic tests, and comprehensive inference tables following the four-case framework.
License:	GPL-3
URL:	https://github.com/muhammedalkhalaf/mvardlurt
BugReports:	https://github.com/muhammedalkhalaf/mvardlurt/issues
Encoding:	UTF-8
RoxygenNote:	7.3.2
Depends:	R (≥ 4.0.0)
Imports:	grDevices, graphics, stats, utils
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-03-09 17:54:26 UTC; acad_
Author:	Muhammad Alkhalaf [aut, cre, cph]
Maintainer:	Muhammad Alkhalaf <muhammedalkhalaf@gmail.com>
Repository:	CRAN
Date/Publication:	2026-03-16 15:50:10 UTC

Multivariate ARDL Unit Root Test

Description

Implements the multivariate autoregressive distributed lag (ARDL) unit root test proposed by Sam, McNown, Goh, and Goh (2024). The test augments the standard ADF regression with lagged levels of a covariate to improve power when cointegration exists. Bootstrap critical values ensure correct size regardless of nuisance parameters.

Details

The main function is mvardlurt, which performs the multivariate ARDL unit root test. The package provides:

• Automatic lag selection via AIC or BIC

• Bootstrap critical values for correct test size

• Three deterministic specifications (none, intercept, intercept + trend)

• Four-case decision framework for inference

• Comprehensive print and summary output

• Diagnostic plots

The test produces two statistics:

• t-statistic: Tests H_0: \pi = 0 (unit root)

• F-statistic: Tests H_0: \delta = 0 (no cointegration)

The four-case framework interprets results as:

• Case I: Both reject \rightarrow Cointegration

• Case II: Reject t, Accept F \rightarrow y may be I(0)

• Case III: Accept t, Reject F \rightarrow Spurious

• Case IV: Both accept \rightarrow No cointegration

Author(s)

Muhammad Alkhalaf

References

Sam, C. Y., McNown, R., Goh, S. K., & Goh, K. L. (2024). A multivariate autoregressive distributed lag unit root test. Studies in Economics and Econometrics, 1-17. doi:10.1080/03796205.2024.2439101

See Also

mvardlurt

Examples

# Generate cointegrated data
set.seed(123)
n <- 200
x <- cumsum(rnorm(n))
y <- 0.5 * x + rnorm(n, sd = 0.5)

# Run the test
result <- mvardlurt(y, x, case = 3, reps = 200)
print(result)

Create a Combined Diagnostic Plot for mvardlurt Objects

Description

Creates a 2x2 panel of diagnostic plots for the multivariate ARDL unit root test including residuals vs fitted, Q-Q plot, residuals over time, and ACF.

Usage

## S3 method for class 'mvardlurt'
autoplot(x, ...)

Arguments

Value

Invisibly returns x.

Author(s)

Muhammad Alkhalaf

See Also

mvardlurt, plot.mvardlurt

Examples

set.seed(123)
n <- 100
x <- cumsum(rnorm(n))
y <- 0.5 * x + rnorm(n, sd = 0.5)

result <- mvardlurt(y, x, reps = 100)
autoplot.mvardlurt(result)

Multivariate ARDL Unit Root Test

Description

Implements the multivariate autoregressive distributed lag (ARDL) unit root test proposed by Sam, McNown, Goh, and Goh (2024). The test augments the standard ADF regression with lagged levels of a covariate (independent variable) to improve power, especially when cointegration exists. Bootstrap critical values ensure correct size regardless of nuisance parameters.

Usage

mvardlurt(y, x, case = 3L, maxlag = 10L, ic = "aic",
          fixlag = NULL, reps = 1000L, level = 0.95,
          seed = 12345L, boot = TRUE)

Arguments

Details

The test estimates the following ARDL regression:

\Delta y_t = \pi y_{t-1} + \delta x_{t-1} + \sum_{j=1}^{p} \gamma_j \Delta y_{t-j} + \sum_{j=1}^{q} \theta_j \Delta x_{t-j} + deterministics + \varepsilon_t

The test produces two statistics:

• t-statistic: Tests H_0: \pi = 0 (unit root in y)

• F-statistic: Tests H_0: \delta = 0 (no cointegration)

Based on the four-case framework (Sam et al., 2024):

• Case I: Reject both \rightarrow Cointegration

• Case II: Reject t, Accept F \rightarrow Degenerate case 1 (y may be I(0))

• Case III: Accept t, Reject F \rightarrow Degenerate case 2 (spurious)

• Case IV: Accept both \rightarrow No cointegration

Value

An object of class "mvardlurt" containing:

Author(s)

Muhammad Alkhalaf

References

Sam, C. Y., McNown, R., Goh, S. K., & Goh, K. L. (2024). A multivariate autoregressive distributed lag unit root test. Studies in Economics and Econometrics, 1-17. doi:10.1080/03796205.2024.2439101

Examples

# Generate example data with cointegration
set.seed(123)
n <- 200
x <- cumsum(rnorm(n))
y <- 0.5 * x + rnorm(n, sd = 0.5)

# Run the test (reduced reps for speed)
result <- mvardlurt(y, x, case = 3, reps = 200)
print(result)

# With fixed lags
result2 <- mvardlurt(y, x, fixlag = c(2, 2), reps = 200)

Plot Method for mvardlurt Objects

Description

Creates diagnostic plots for the multivariate ARDL unit root test.

Usage

## S3 method for class 'mvardlurt'
plot(x, which = c(1, 2, 3, 4),
     ask = (length(which) > 1 && dev.interactive()), ...)

Arguments

Value

Invisibly returns x.

Author(s)

Muhammad Alkhalaf

See Also

mvardlurt, autoplot.mvardlurt

Examples

set.seed(123)
n <- 100
x <- cumsum(rnorm(n))
y <- 0.5 * x + rnorm(n, sd = 0.5)

result <- mvardlurt(y, x, reps = 100)

# Default diagnostic plots
plot(result, ask = FALSE)

# IC surface plot
plot(result, which = 6)

Methods for mvardlurt Objects

Description

Print, summary, and accessor methods for objects of class "mvardlurt".

Usage

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

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

## S3 method for class 'mvardlurt'
coef(object, ...)

## S3 method for class 'mvardlurt'
residuals(object, ...)

## S3 method for class 'mvardlurt'
fitted(object, ...)

Arguments

Value

print and summary invisibly return x/object.

coef returns a named numeric vector with pi, delta, and lr_mult.

residuals returns the numeric vector of residuals from the fitted model.

fitted returns the numeric vector of fitted values.

Author(s)

Muhammad Alkhalaf

See Also

mvardlurt

Examples

set.seed(123)
n <- 100
x <- cumsum(rnorm(n))
y <- 0.5 * x + rnorm(n, sd = 0.5)

result <- mvardlurt(y, x, reps = 100)

# Print method
print(result)

# Summary method
summary(result)

# Extract coefficients
coef(result)

# Extract residuals
head(residuals(result))

# Extract fitted values
head(fitted(result))