Comprehensive ARDL: Panel, Bootstrap and Fourier Methods

A unified framework for Autoregressive Distributed Lag (ARDL) modeling and cointegration analysis. Implements Panel ARDL with Pooled Mean Group (PMG), Mean Group (MG), and Dynamic Fixed Effects (DFE) estimators following Pesaran, Shin and Smith (1999) . Provides the bounds test of Pesaran, Shin and Smith (2001) with the critical values of Kripfganz and Schneider (2020) and with recursive bootstrap critical values following Bertelli, Vacca and Zoia (2022) and McNown, Sam and Goh (2018) . Includes Quantile Nonlinear ARDL (QNARDL) combining distributional and asymmetric effects based on Shin, Yu and Greenwood-Nimmo (2014) , Fourier ARDL for modeling smooth structural breaks following Enders and Lee (2012) , and Fourier (bootstrap) nonlinear ARDL. Features include Augmented ARDL (AARDL) with deferred t and F tests, Multiple-Threshold NARDL for complex asymmetries, Rolling/Recursive ARDL for time-varying relationships, and Panel NARDL for nonlinear panel cointegration. All methods include comprehensive diagnostics, publication-ready outputs, and visualization tools.

ardlverse

Overview

ardlverse is a comprehensive R package for Autoregressive Distributed Lag (ARDL) modeling and cointegration analysis. It provides unified tools for:

• 📊 Panel ARDL: Pooled Mean Group (PMG), Mean Group (MG), and Dynamic Fixed Effects (DFE) estimators
• 🎰 Bootstrap ARDL: Bootstrap-based bounds testing for small samples
• 📈 Quantile NARDL: Quantile Nonlinear ARDL combining distributional and asymmetric effects
• 🌊 Fourier ARDL: Smooth structural breaks using Fourier approximation
• 🔍 Diagnostics: Comprehensive model diagnostics and visualization

Installation

# Install from CRAN (once available)
install.packages("ardlverse")

# Or install development version from GitHub
# install.packages("devtools")
devtools::install_github("muhammedalkhalaf/ardlverse")

Quick Start

Panel ARDL with PMG Estimator

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)

Bootstrap Bounds Test

# 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.

Quantile Nonlinear ARDL

# 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)

Fourier ARDL

# 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)

Model Diagnostics

# Run comprehensive diagnostics
diag <- ardl_diagnostics(f_model)
summary(diag)
plot(diag)

Augmented ARDL (New in v1.1.0)

# 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)

Multiple-Threshold NARDL (New in v1.1.0)

# 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")

Rolling ARDL (New in v1.1.0)

# 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 NARDL (New in v1.1.0)

# Panel data with asymmetric effects
pnardl_model <- pnardl(
  y ~ x1 + x2,
  data = panel_data,
  id = "country",
  time = "year",
  estimator = "pmg"
)
summary(pnardl_model)

Main Functions

Core ARDL Models

New in v1.1.0: ARDL Extensions

Supporting Functions

Theoretical Background

Panel ARDL (Pesaran, Shin and Smith, 1999)

The PMG estimator allows for heterogeneous short-run dynamics while constraining long-run coefficients to be equal across groups:

$$\Delta y_{it} = \phi_i (y_{i,t-1} - \theta' x_{it}) + \sum_{j=1}^{p-1} \lambda_{ij} \Delta y_{i,t-j} + \sum_{j=0}^{q-1} \delta'{ij} \Delta x{i,t-j} + \mu_i + \varepsilon_{it}$$

QNARDL (Cho, Kim and Shin, 2015 + Shin, Yu and Greenwood-Nimmo, 2014)

Combines quantile regression with asymmetric decomposition:

$$x^+t = \sum{j=1}^{t} \max(\Delta x_j, 0), \quad x^-t = \sum{j=1}^{t} \min(\Delta x_j, 0)$$

Fourier ARDL (Banerjee, Arcabic and Lee, 2017)

Captures smooth structural breaks using Fourier approximation:

$$f_t = \sum_{k=1}^{K} [a_k \sin(2\pi k t/T) + b_k \cos(2\pi k t/T)]$$

References

• 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.

Author

Muhammad Alkhalaf

• ORCID: 0009-0002-2677-9246
• Email: [email protected]
• Website: rufyqelngeh.com

License

GPL-3