ardlverse is a comprehensive R package for Autoregressive Distributed Lag (ARDL) modeling and cointegration analysis. It provides unified tools for:
# Install from CRAN (once available)
install.packages("ardlverse")
# Or install development version from GitHub
# install.packages("devtools")
devtools::install_github("muhammedalkhalaf/ardlverse")library(ardlverse)
# Generate example data
data <- generate_panel_data(n_groups = 10, n_time = 50)
# Estimate PMG model
pmg_model <- panel_ardl(
gdp ~ inflation + investment,
data = data,
id = "country",
time = "year",
p = 1, q = 1,
estimator = "pmg"
)
summary(pmg_model)
# Hausman test: PMG vs MG
hausman_test(pmg_model)# Generate time series data
ts_data <- generate_ts_data(n = 100)
# Bootstrap bounds test
boot_test <- boot_ardl(
gdp ~ inflation + investment,
data = ts_data,
p = 2, q = 2,
case = 3,
nboot = 2000
)
summary(boot_test)
plot(boot_test)Since version 2.1.0 the bootstrap is recursive (y* and x* are
generated from the estimated model under the null): separate nulls for
Fov, t and Find following Bertelli, Vacca and Zoia (2022) by default, or
the joint null of McNown, Sam and Goh (2018) with
nulls = "joint". Cointegration is concluded only when Fov,
t and Find all reject. The same engine is used by the bootstrap types of
aardl(), by mtnardl(bootstrap = TRUE) and by
fbnardl(type = "fbnardl"). With Fourier terms no valid
bounds exist; use the bootstrap.
# Generate oil price data
oil <- generate_oil_data(n = 200)
# Estimate QNARDL
qnardl_model <- qnardl(
gasoline ~ oil_price + exchange_rate,
data = oil,
tau = c(0.1, 0.25, 0.5, 0.75, 0.9),
p = 2, q = 2
)
summary(qnardl_model)
plot(qnardl_model, var = "oil_price")
# Test for asymmetry
asymmetry_test(qnardl_model, var = "oil_price")
# Dynamic multipliers
dynamic_multipliers(qnardl_model, var = "oil_price", tau = 0.5)# Estimate Fourier ARDL with automatic frequency selection
f_model <- fourier_ardl(
gdp ~ investment + trade,
data = ts_data,
p = 2, q = 2,
selection = "aic"
)
summary(f_model)
plot(f_model)
fourier_bounds_test(f_model)# Run comprehensive diagnostics
diag <- ardl_diagnostics(f_model)
summary(diag)
plot(diag)# Augmented ARDL with deferred tests
aardl_model <- aardl(
gdp ~ inflation + investment,
data = ts_data,
type = "linear", # or "nardl", "fourier", "fbnardl"
p = 2, q = 2
)
summary(aardl_model)# Decompose into 4 regimes: large/small positive/negative changes
mt_model <- mtnardl(
consumption ~ oil_price,
data = oil,
thresholds = c(-0.05, 0, 0.05),
p = 2, q = 2
)
summary(mt_model)
plot(mt_model, type = "multipliers")# Time-varying bounds test
roll_model <- rardl(
gdp ~ investment + trade,
data = ts_data,
method = "rolling",
window = 60
)
summary(roll_model)
plot(roll_model, type = "all")# Panel data with asymmetric effects
pnardl_model <- pnardl(
y ~ x1 + x2,
data = panel_data,
id = "country",
time = "year",
estimator = "pmg"
)
summary(pnardl_model)| Function | Description |
|---|---|
panel_ardl() |
Panel ARDL with PMG, MG, DFE estimators |
boot_ardl() |
Bootstrap ARDL bounds test |
qnardl() |
Quantile Nonlinear ARDL |
fourier_ardl() |
Fourier ARDL for structural breaks |
| Function | Description |
|---|---|
aardl() |
Augmented ARDL with deferred t and F tests (8 sub-models) |
mtnardl() |
Multiple-Threshold NARDL for complex asymmetries |
fbnardl() |
Fourier (bootstrap) nonlinear ARDL with frequency and lag selection |
rardl() |
Rolling and Recursive ARDL for time-varying relationships |
pnardl() |
Panel Nonlinear ARDL (PMG/MG/DFE with asymmetry) |
| Function | Description |
|---|---|
ardl_diagnostics() |
Comprehensive model diagnostics |
hausman_test() |
Hausman test for PMG vs MG |
asymmetry_test() |
Test for long-run asymmetry |
dynamic_multipliers() |
Cumulative dynamic multipliers |
pss_critical_values() |
PSS (2001) critical value tables |
The PMG estimator allows for heterogeneous short-run dynamics while constraining long-run coefficients to be equal across groups:
\[\Delta y_{it} = \phi_i (y_{i,t-1} - \theta' x_{it}) + \sum_{j=1}^{p-1} \lambda_{ij} \Delta y_{i,t-j} + \sum_{j=0}^{q-1} \delta'_{ij} \Delta x_{i,t-j} + \mu_i + \varepsilon_{it}\]
Combines quantile regression with asymmetric decomposition:
\[x^+_t = \sum_{j=1}^{t} \max(\Delta x_j, 0), \quad x^-_t = \sum_{j=1}^{t} \min(\Delta x_j, 0)\]
Captures smooth structural breaks using Fourier approximation:
\[f_t = \sum_{k=1}^{K} [a_k \sin(2\pi k t/T) + b_k \cos(2\pi k t/T)]\]
Pesaran, M. H., Shin, Y. and Smith, R. P. (1999). Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association, 94(446), 621-634.
Pesaran, M. H., Shin, Y. and Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16(3), 289-326.
Shin, Y., Yu, B. and Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In Festschrift in Honor of Peter Schmidt (pp. 281-314). Springer.
Cho, J. S., Kim, T. H. and Shin, Y. (2015). Quantile cointegration in the autoregressive distributed-lag modeling framework. Journal of Econometrics, 188(1), 281-300.
Banerjee, P., Arcabic, V. and Lee, H. (2017). Fourier ADL cointegration test to approximate smooth breaks with new evidence from crude oil market. Economic Modelling, 67, 114-124.
Bertelli, S., Vacca, G. and Zoia, M. (2022). Bootstrap cointegration tests in ARDL models. Economic Modelling, 116, 105987.
McNown, R., Sam, C. Y. and Goh, S. K. (2018). Bootstrapping the autoregressive distributed lag test for cointegration. Applied Economics, 50(13), 1509-1521.
Sam, C. Y., McNown, R. and Goh, S. K. (2019). An augmented autoregressive distributed lag bounds test for cointegration. Economic Modelling, 80, 130-141.
Muhammad Alkhalaf - ORCID: 0009-0002-2677-9246 - Email: contact@rufyqelngeh.com - Website: rufyqelngeh.com
GPL-3