Comprehensive ARDL: Panel, Bootstrap and Fourier Methods.

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)

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 & 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 & Shin, 2015 + Shin, Yu & 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 & 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., & 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., & 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., & 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., & Shin, Y. (2015). Quantile cointegration in the autoregressive distributed-lag modeling framework. Journal of Econometrics, 188(1), 281-300.

• 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.

• McNown, R., Sam, C. Y., & Goh, S. K. (2018). Bootstrapping the autoregressive distributed lag test for cointegration. Applied Economics, 50(13), 1509-1521.

• Sam, C. Y., McNown, R., & 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