Type:	Package
Title:	Comprehensive ARDL Modeling Framework: Panel, Bootstrap, Quantile-Nonlinear, and Fourier Extensions
Version:	1.1.2
Date:	2026-02-26
Description:	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 & Smith (1999) <doi:10.1002/jae.616>. Provides bootstrap-based bounds testing per Pesaran, Shin & Smith (2001) <doi:10.1002/jae.616>. Includes Quantile Nonlinear ARDL (QNARDL) combining distributional and asymmetric effects based on Shin, Yu & Greenwood-Nimmo (2014) <doi:10.1007/978-1-4899-8008-3_9>, and Fourier ARDL for modeling smooth structural breaks following Enders & Lee (2012) <doi:10.1016/j.econlet.2012.05.019>. 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.
License:	GPL-3
URL:	https://github.com/muhammedalkhalaf/ardlverse
BugReports:	https://github.com/muhammedalkhalaf/ardlverse/issues
Encoding:	UTF-8
LazyData:	true
Depends:	R (≥ 4.0.0)
Imports:	stats, MASS, quantreg, lmtest, ggplot2, gridExtra, graphics, grDevices
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown, covr
RoxygenNote:	7.3.3
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-03-07 04:24:37 UTC; acad_
Author:	Muhammad Abdullah Alkhalaf [aut, cre], Merwan Roudane [ctb] (Original Stata implementations)
Maintainer:	Muhammad Abdullah Alkhalaf <muhammedalkhalaf@gmail.com>
Repository:	CRAN
Date/Publication:	2026-03-11 19:50:02 UTC

Comprehensive ARDL Modeling Framework

Description

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. Provides bootstrap-based bounds testing for small samples, Quantile Nonlinear ARDL (QNARDL) combining distributional and asymmetric effects, and Fourier ARDL for modeling smooth structural breaks.

Details

The main functions are:

• 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

• ardl_diagnostics: Comprehensive model diagnostics

Supporting functions:

• hausman_test: PMG vs MG comparison

• asymmetry_test: Long-run asymmetry test

• dynamic_multipliers: Cumulative multipliers

• pss_critical_values: PSS (2001) critical values

Data generation for examples:

• generate_panel_data: Panel data

• generate_ts_data: Time series data

• generate_oil_data: Oil/gasoline price data

Author(s)

Muhammad Abdullah Alkhalaf <muhammedalkhalaf@gmail.com>

Maintainer: Muhammad Abdullah Alkhalaf <muhammedalkhalaf@gmail.com>

References

Pesaran, M. H., Shin, Y., & Smith, R. P. (1999). Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association.

Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics.

Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework.

Cho, J. S., Kim, T. H., & Shin, Y. (2015). Quantile cointegration in the autoregressive distributed-lag modeling framework. Journal of Econometrics.

Banerjee, P., Arcabic, V., & Lee, H. (2017). Fourier ADL cointegration test. Economic Modelling.

Examples

## Not run: 
# Panel ARDL
data <- generate_panel_data()
model <- panel_ardl(gdp ~ inflation + investment, data = data,
                    id = "country", time = "year", estimator = "pmg")
summary(model)

# Bootstrap bounds test
ts_data <- generate_ts_data()
boot <- boot_ardl(gdp ~ investment, data = ts_data, nboot = 1000)
summary(boot)

# QNARDL
oil <- generate_oil_data()
qmodel <- qnardl(gasoline ~ oil_price, data = oil, tau = c(0.25, 0.5, 0.75))
asymmetry_test(qmodel, var = "oil_price")

## End(Not run)

AARDL Bootstrap Procedure

Description

AARDL Bootstrap Procedure

Usage

.aardl_bootstrap(dy, design, n_level, k, nboot)

AARDL Conclusion

Description

AARDL Conclusion

Usage

.aardl_conclusion(F_pss, t_dep, F_ind, cv, boot = NULL)

AARDL Critical Values

Description

AARDL Critical Values

Usage

.aardl_critical_values(k, case, n)

ARCH Test

Description

ARCH Test

Usage

.arch_test(resid, lags)

Bootstrap Bounds Test

Description

Bootstrap Bounds Test

Usage

.bootstrap_bounds(ardl_data, model_ur, case, k, nboot, parallel, ncores)

Bounds Test Conclusion

Description

Bounds Test Conclusion

Usage

.bounds_conclusion(F_stat, t_stat, cv_F, cv_t, k, case)

Breusch-Godfrey Serial Correlation Test

Description

Breusch-Godfrey Serial Correlation Test

Usage

.breusch_godfrey_test(resid, order = 2)

Breusch-Pagan Heteroskedasticity Test

Description

Breusch-Pagan Heteroskedasticity Test

Usage

.breusch_pagan_test(model)

Cluster Nearby Breaks

Description

Cluster Nearby Breaks

Usage

.cluster_breaks(breaks, min_gap = 5)

Compute Overall F-statistic

Description

Compute Overall F-statistic

Usage

.compute_F_overall(model_ur, model_r, k, case)

Compute F-statistic for Bounds Test

Description

Compute F-statistic for Bounds Test

Usage

.compute_F_stat(model_ur, model_r, k, case)

Compute Multiple-Threshold Dynamic Multipliers

Description

Compute Multiple-Threshold Dynamic Multipliers

Usage

.compute_mt_multipliers(
  coefs,
  ec_coef,
  regime_names,
  k_total,
  n_regimes,
  horizons = 30
)

Compute PMG Standard Errors

Description

Internal function to compute standard errors for PMG estimator

Usage

.compute_pmg_se(group_data, theta, n_groups)

Compute t-statistic for EC Coefficient

Description

Compute t-statistic for EC Coefficient

Usage

.compute_t_stat(model_ur)

Create Fourier Terms

Description

Create Fourier Terms

Usage

.create_fourier_terms(n, k)

CUSUM Test

Description

CUSUM Test

Usage

.cusum_test(resid)

CUSUM of Squares Test

Description

CUSUM of Squares Test

Usage

.cusumsq_test(resid)

Decompose Variables for Asymmetric Analysis

Description

Decompose Variables for Asymmetric Analysis

Usage

.decompose_asymmetric(X, threshold = 0)

Demean Panel Data

Description

Demean Panel Data

Usage

.demean_panel(data, y_var, x_vars, id)

Detect Structural Breaks

Description

Detect Structural Breaks

Usage

.detect_ardl_breaks(F_stats, ec_coefs, lr_coefs)

Detect Fourier Structural Breaks

Description

Detect Fourier Structural Breaks

Usage

.detect_fourier_breaks(fourier_coefs, n, k)

Estimate Restricted ARDL Model

Description

Estimate Restricted ARDL Model

Usage

.estimate_ardl_restricted(ardl_data, case)

Estimate Unrestricted ARDL Model

Description

Estimate Unrestricted ARDL Model

Usage

.estimate_ardl_unrestricted(ardl_data, case)

Estimate ARDL for Single Window

Description

Estimate ARDL for Single Window

Usage

.estimate_ardl_window(data, y_var, x_vars, p, q, case)

Dynamic Fixed Effects Estimator

Description

Internal function for DFE estimation

Usage

.estimate_dfe(data, y_var, x_vars, id, time, p, q, trend)

Internal Fourier ARDL Estimation

Description

Internal Fourier ARDL Estimation

Usage

.estimate_fourier_ardl(data, y_var, x_vars, p, q, k, case)

Mean Group Estimator

Description

Internal function for MG estimation

Usage

.estimate_mg(data, y_var, x_vars, id, time, p, q, trend)

Internal MG estimation

Description

Internal MG estimation

Usage

.estimate_mg_internal(group_data, groups, k_x, trend)

Pooled Mean Group Estimator

Description

Internal function for PMG estimation

Usage

.estimate_pmg(data, y_var, x_vars, id, time, p, q, trend, maxiter, tol)

Estimate QNARDL for Single Quantile

Description

Estimate QNARDL for Single Quantile

Usage

.estimate_qnardl_tau(model_data, y_col, x_cols, tau)

Estimate Unit NARDL

Description

Estimate Unit NARDL

Usage

.estimate_unit_nardl(data, y_var, x_vars, p, q)

Extract Long-Run Coefficients

Description

Extract Long-Run Coefficients

Usage

.extract_long_run(results_by_tau, level_vars, tau)

Generate Fourier Terms

Description

Generate Fourier Terms

Usage

.generate_fourier_terms(n, k)

Jarque-Bera Test

Description

Jarque-Bera Test

Usage

.jarque_bera_test(resid)

Make Regime Names

Description

Make Regime Names

Usage

.make_regime_names(x_vars, thresholds)

Manual Breusch-Godfrey Test

Description

Manual Breusch-Godfrey Test

Usage

.manual_bg_test(resid, lags)

Manual Breusch-Pagan Test

Description

Manual Breusch-Pagan Test

Usage

.manual_bp_test(resid, fitted)

Multiple-Threshold Decomposition

Description

Multiple-Threshold Decomposition

Usage

.mt_decompose(X, thresholds)

MT-NARDL Bootstrap

Description

MT-NARDL Bootstrap

Usage

.mtnardl_bootstrap(dy, design, n_level, nboot)

MT-NARDL Bounds Test Conclusion

Description

MT-NARDL Bounds Test Conclusion

Usage

.mtnardl_bounds_conclusion(F_stat, t_stat, cv, boot = NULL)

Package Startup

Description

Functions run on package load

Usage

.onLoad(libname, pkgname)

Panel Hausman Test

Description

Panel Hausman Test

Usage

.panel_hausman_test(pmg_result, mg_result)

Panel NARDL Decomposition

Description

Panel NARDL Decomposition

Usage

.panel_nardl_decompose(data, x_vars, id, time, threshold)

Panel NARDL Bootstrap

Description

Panel NARDL Bootstrap

Usage

.pnardl_bootstrap(
  data,
  y_var,
  x_vars,
  id,
  time,
  p,
  q,
  estimator,
  effect,
  nboot,
  groups
)

Panel NARDL DFE Estimator

Description

Panel NARDL DFE Estimator

Usage

.pnardl_dfe(data, y_var, x_vars, orig_vars, id, time, p, q, effect, k)

Panel NARDL MG Estimator

Description

Panel NARDL MG Estimator

Usage

.pnardl_mg(data, y_var, x_vars, orig_vars, id, time, p, q, effect, k, groups)

Panel NARDL PMG Estimator

Description

Panel NARDL PMG Estimator

Usage

.pnardl_pmg(data, y_var, x_vars, orig_vars, id, time, p, q, effect, k)

Prepare ARDL Data

Description

Internal function to prepare data for ARDL estimation

Usage

.prepare_ardl_data(data, y_var, x_vars, time, p, q, trend)

Prepare Time Series Data for ARDL

Description

Prepare Time Series Data for ARDL

Usage

.prepare_ardl_ts_data(data, y_var, x_vars, p, q, case)

Prepare Fourier ARDL Data

Description

Prepare Fourier ARDL Data

Usage

.prepare_fourier_data(data, y_var, x_vars, p, q, k, case)

Prepare QNARDL Data with Partial Sum Decomposition

Description

Prepare QNARDL Data with Partial Sum Decomposition

Usage

.prepare_qnardl_data(data, y_var, x_vars, decompose, p, q, trend)

Select Optimal Thresholds

Description

Select Optimal Thresholds

Usage

.select_optimal_thresholds(y, X, n_thresholds, p, q, case)

Significance Stars Helper

Description

Significance Stars Helper

Usage

.signif_stars(p)

Stack Long-Run Data for PMG

Description

Stack Long-Run Data for PMG

Usage

.stack_lr_data(data, y_var, x_vars, id, time, phi, sr_results, groups)

Test for Long-Run Asymmetry

Description

Test for Long-Run Asymmetry

Usage

.test_asymmetry(results_by_tau, var, tau)

Test Panel Asymmetry

Description

Test Panel Asymmetry

Usage

.test_panel_asymmetry(result, x_vars, k)

Test Regime Asymmetry

Description

Test Regime Asymmetry

Usage

.test_regime_asymmetry(
  coefs,
  vcov_mat,
  x_vars,
  regime_names,
  thresholds,
  k_total
)

Augmented ARDL Bounds Test (AARDL)

Description

Implements the Augmented ARDL bounds testing approach with deferred t and F tests for cointegration analysis.

Usage

aardl(formula, data, p = 1, q = 1, case = 3,
      type = c("linear", "nardl", "fourier", "fnardl",
               "bootstrap", "bnardl", "fbootstrap", "fbnardl"),
      nboot = 2000, fourier_k = 1, threshold = 0, seed = NULL)

## S3 method for class 'aardl'
print(x, ...)
## S3 method for class 'aardl'
summary(object, ...)

Arguments

Details

The Augmented ARDL (AARDL) approach extends the standard ARDL bounds test by implementing additional diagnostic tests proposed by Sam, McNown & Goh (2019). This addresses potential weaknesses in the PSS bounds test by adding:

• Deferred t-test (t_dep): Tests significance of lagged dependent variable

• Deferred F-test (F_ind): Tests joint significance of independent variables

• Overall F-test with all deferred conditions

The function supports 8 sub-models including standard ARDL, NARDL, Fourier ARDL, and their bootstrap variants.

Value

An object of class "aardl" containing:

References

Sam, C. Y., McNown, R., & Goh, S. K. (2019). An augmented autoregressive distributed lag bounds test for cointegration. Economic Modelling, 80, 130-141.

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

See Also

boot_ardl, qnardl, fourier_ardl

Examples

## Not run: 
# Generate example data
data <- generate_ts_data(n = 200)

# Standard Augmented ARDL
result <- aardl(y ~ x1 + x2, data = data, p = 2, q = 2, case = 3)
summary(result)

# Augmented NARDL (nonlinear)
result_nardl <- aardl(y ~ x1 + x2, data = data, type = "nardl")
summary(result_nardl)

# Fourier Augmented ARDL with bootstrap
result_fb <- aardl(y ~ x1, data = data, type = "fbootstrap", nboot = 1000)

## End(Not run)

ARDL Model Diagnostics

Description

Comprehensive diagnostic tests for ARDL models.

Usage

ardl_diagnostics(model, lags = 4, arch_lags = 4)

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

## S3 method for class 'ardl_diagnostics'
plot(x, which = 1:4, ...)

Arguments

Details

This function performs a battery of diagnostic tests:

• Serial Correlation: Breusch-Godfrey LM test and Ljung-Box test

• Heteroskedasticity: Breusch-Pagan and ARCH tests

• Normality: Jarque-Bera and Shapiro-Wilk tests

• Functional Form: RESET test

• Stability: CUSUM and CUSUMSQ tests

Value

An object of class "ardl_diagnostics" containing:

See Also

fourier_ardl, boot_ardl

Examples

## Not run: 
# Estimate a model
data <- generate_ts_data(n = 100)
model <- fourier_ardl(gdp ~ investment, data = data)

# Run diagnostics
diag <- ardl_diagnostics(model)
summary(diag)
plot(diag)

## End(Not run)

Test Asymmetry in QNARDL Model

Description

Perform Wald test for long-run asymmetry in QNARDL models.

Usage

asymmetry_test(object, var)

Arguments

Details

Tests the null hypothesis that positive and negative long-run effects are equal (H0: theta+ = theta-) against the alternative of asymmetric effects (H1: theta+ != theta-).

The test is performed separately for each quantile.

Value

A data frame with test results by quantile:

See Also

qnardl, dynamic_multipliers

Examples

## Not run: 
data <- generate_oil_data(n = 200)

model <- qnardl(
  gasoline ~ oil_price,
  data = data,
  tau = c(0.25, 0.5, 0.75)
)

asymmetry_test(model, var = "oil_price")

## End(Not run)

Bootstrap ARDL Bounds Test

Description

Perform bounds test for cointegration with bootstrap critical values.

Usage

boot_ardl(formula, data, p = 1, q = 1, case = 3,
          nboot = 2000, seed = NULL, 
          parallel = FALSE, ncores = 2)

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

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

## S3 method for class 'boot_ardl'
plot(x, which = "both", ...)

Arguments

Details

This function implements bootstrap-based inference for the ARDL bounds test, which is particularly useful for small samples where asymptotic critical values may be unreliable.

Case specifications:

• 1: No intercept, no trend

• 2: Restricted intercept, no trend

• 3: Unrestricted intercept, no trend (default)

• 4: Unrestricted intercept, restricted trend

• 5: Unrestricted intercept, unrestricted trend

Value

An object of class "boot_ardl" containing:

References

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

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.

See Also

pss_critical_values, generate_ts_data

Examples

## Not run: 
# Generate example data
data <- generate_ts_data(n = 100)

# Bootstrap bounds test
boot_test <- boot_ardl(
  gdp ~ inflation + investment,
  data = data,
  p = 2, q = 2,
  nboot = 1000
)
summary(boot_test)
plot(boot_test)

## End(Not run)

Dynamic Multipliers for QNARDL

Description

Compute and plot cumulative dynamic multipliers for QNARDL models.

Usage

dynamic_multipliers(object, var, tau = 0.5, horizon = 20)

Arguments

Details

Computes the cumulative dynamic multipliers showing how the effect of a unit change in x accumulates over time towards the long-run equilibrium.

Separate multipliers are computed for positive and negative changes, allowing visualization of asymmetric adjustment paths.

Value

A data frame with:

See Also

qnardl, asymmetry_test

Examples

## Not run: 
data <- generate_oil_data(n = 200)

model <- qnardl(
  gasoline ~ oil_price,
  data = data,
  tau = c(0.25, 0.5, 0.75)
)

# Plot dynamic multipliers at median
dynamic_multipliers(model, var = "oil_price", tau = 0.5, horizon = 30)

## End(Not run)

Fourier ARDL Model

Description

Estimate ARDL models with Fourier terms for smooth structural breaks.

Usage

fourier_ardl(formula, data, p = 1, q = 1, k = 1, case = 3,
             selection = c("fixed", "aic", "bic"))

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

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

## S3 method for class 'fourier_ardl'
plot(x, which = "both", ...)

Arguments

Details

This function implements the Fourier ARDL approach that captures smooth structural changes using trigonometric functions. The Fourier terms approximate unknown structural breaks without requiring prior specification of break dates.

The Fourier terms are defined as:

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

where K is the number of frequencies and T is the sample size.

Value

An object of class "fourier_ardl" containing:

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.

Enders, W., & Lee, J. (2012). A unit root test using a Fourier series to approximate smooth breaks. Oxford Bulletin of Economics and Statistics, 74(4), 574-599.

See Also

fourier_bounds_test, generate_ts_data

Examples

## Not run: 
# Generate example data
data <- generate_ts_data(n = 100)

# Estimate Fourier ARDL with automatic selection
model <- fourier_ardl(
  gdp ~ investment + trade,
  data = data,
  selection = "aic"
)
summary(model)
plot(model)

## End(Not run)

Fourier ARDL Bounds Test

Description

Perform bounds test with Fourier-adjusted critical values.

Usage

fourier_bounds_test(object)

Arguments

Details

Performs the bounds test for cointegration using critical values adjusted for the presence of Fourier terms. The critical values account for the additional parameters estimated.

Value

A list containing:

See Also

fourier_ardl, pss_critical_values

Examples

## Not run: 
data <- generate_ts_data(n = 100)

model <- fourier_ardl(
  gdp ~ investment,
  data = data,
  k = 1
)

fourier_bounds_test(model)

## End(Not run)

Generate Oil Price Data

Description

Generate simulated oil and gasoline price data with asymmetric effects.

Usage

generate_oil_data(n = 200, seed = 789)

Arguments

Details

Generates a simulated dataset exhibiting the "rockets and feathers" phenomenon where gasoline prices respond more quickly to oil price increases than decreases. Suitable for demonstrating QNARDL methods and asymmetry testing.

Value

A data frame with columns:

See Also

qnardl, asymmetry_test

Examples

# Generate oil price data
oil <- generate_oil_data(n = 200)
head(oil)

# Plot prices
plot(oil$week, oil$oil_price, type = "l", col = "blue",
     main = "Oil and Gasoline Prices")
lines(oil$week, oil$gasoline/4, col = "red")  # Scaled for comparison

Generate Example Panel Data

Description

Generate simulated panel data for examples and testing.

Usage

generate_panel_data(n_groups = 10, n_time = 50, seed = 123)

Arguments

Details

Generates a simulated panel dataset with cointegrated variables suitable for demonstrating panel ARDL methods. The data generating process includes country-specific fixed effects and error correction dynamics.

Value

A data frame with columns:

See Also

panel_ardl, generate_ts_data

Examples

# Generate panel data for 5 countries, 30 years
panel <- generate_panel_data(n_groups = 5, n_time = 30)
head(panel)

# Check dimensions
table(panel$country)

Generate Example Time Series Data

Description

Generate simulated time series data for examples and testing.

Usage

generate_ts_data(n = 100, seed = 456)

Arguments

Details

Generates a simulated time series dataset with cointegrated variables and a smooth structural break (modeled via Fourier component). Suitable for demonstrating Fourier ARDL and bootstrap bounds testing methods.

Value

A data frame with columns:

See Also

fourier_ardl, boot_ardl, generate_panel_data

Examples

# Generate 100 quarters of data
ts_data <- generate_ts_data(n = 100)
head(ts_data)

# Plot GDP series
plot(ts_data$quarter, ts_data$gdp, type = "l",
     main = "Simulated GDP with Structural Break")

Hausman Test for PMG vs MG

Description

Perform Hausman test comparing PMG and MG estimators.

Usage

hausman_test(pmg_model, mg_model = NULL, data = NULL)

Arguments

Details

The Hausman test examines whether the long-run homogeneity assumption of the PMG estimator is valid. Under the null hypothesis of homogeneity, both PMG and MG are consistent, but PMG is efficient. Under the alternative, only MG is consistent.

Value

A list containing:

See Also

panel_ardl

Examples

## Not run: 
data <- generate_panel_data(n_groups = 10, n_time = 50)

pmg <- panel_ardl(gdp ~ inflation + investment, data = data,
                  id = "country", time = "year", estimator = "pmg")

mg <- panel_ardl(gdp ~ inflation + investment, data = data,
                 id = "country", time = "year", estimator = "mg")

hausman_test(pmg, mg)

## End(Not run)

Time Series Macroeconomic Data

Description

A simulated time series dataset of macroeconomic variables for a single country over 100 quarters.

Usage

macro_data

Format

A data frame with 100 rows and 5 variables: quarter, gdp, inflation, investment, trade.

Source

Simulated data for demonstration purposes

Examples

data(macro_data)
head(macro_data)

Simulated Macroeconomic Panel Data

Description

A simulated panel dataset of macroeconomic variables for 10 countries over 50 years.

Usage

macro_panel

Format

A data frame with 500 rows and 6 variables: country, year, gdp, inflation, investment, trade.

Source

Simulated data for demonstration purposes

Examples

data(macro_panel)
head(macro_panel)

# Estimate Panel ARDL
model <- panel_ardl(
  gdp ~ inflation + investment,
  data = macro_panel,
  id = "country",
  time = "year",
  estimator = "pmg"
)

Multiple-Threshold Nonlinear ARDL (MT-NARDL)

Description

Extends NARDL to allow multiple threshold decomposition for capturing complex asymmetric relationships.

Usage

mtnardl(formula, data, thresholds = c(0), p = 1, q = 1, case = 3,
        auto_select = FALSE, n_thresholds = 2,
        bootstrap = FALSE, nboot = 2000, seed = NULL)

## S3 method for class 'mtnardl'
print(x, ...)
## S3 method for class 'mtnardl'
summary(object, ...)
## S3 method for class 'mtnardl'
plot(x, type = c("multipliers", "asymmetry"), ...)

Arguments

Details

The Multiple-Threshold NARDL (MT-NARDL) model extends the standard NARDL framework by allowing decomposition of variables into multiple regimes based on user-specified thresholds. This captures more nuanced asymmetric effects beyond simple positive/negative decomposition.

For example, with thresholds c(-0.02, 0, 0.02), a variable is decomposed into:

• Large decreases (< -2%)

• Small decreases (-2% to 0)

• Small increases (0 to 2%)

• Large increases (> 2%)

Value

An object of class "mtnardl" containing:

References

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.

See Also

qnardl, aardl

Examples

## Not run: 
# Generate example data
data <- generate_oil_data(n = 300)

# Standard NARDL (single threshold at 0)
result1 <- mtnardl(consumption ~ oil_price, data = data)

# Multiple thresholds for different shock sizes
result2 <- mtnardl(
  consumption ~ oil_price,
  data = data,
  thresholds = c(-0.05, 0, 0.05)
)
summary(result2)
plot(result2, type = "multipliers")

# Auto-select optimal thresholds
result3 <- mtnardl(
  consumption ~ oil_price,
  data = data,
  auto_select = TRUE,
  n_thresholds = 2
)

## End(Not run)

Oil Price and Gasoline Data

Description

Weekly data on oil prices and retail gasoline prices, suitable for demonstrating asymmetric price transmission.

Usage

oil_data

Format

A data frame with 200 rows and 4 variables: week, gasoline, oil_price, exchange_rate.

Source

Simulated data for demonstration purposes

Examples

data(oil_data)

# Test for asymmetric price transmission
model <- qnardl(
  gasoline ~ oil_price + exchange_rate,
  data = oil_data,
  tau = c(0.25, 0.5, 0.75)
)
asymmetry_test(model, var = "oil_price")

Panel ARDL Estimation

Description

Estimate Panel ARDL models with Pooled Mean Group (PMG), Mean Group (MG), and Dynamic Fixed Effects (DFE) estimators.

Usage

panel_ardl(formula, data, id, time, p = 1, q = 1,
           estimator = c("pmg", "mg", "dfe"),
           ec = TRUE, trend = FALSE,
           maxiter = 100, tol = 1e-5)

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

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

Arguments

Details

This function implements the panel ARDL framework of Pesaran, Shin & Smith (1999) for estimating long-run relationships in dynamic heterogeneous panels.

Three estimators are available:

• PMG: Constrains long-run coefficients to be equal across groups while allowing short-run coefficients to vary.

• MG: Estimates separate regressions for each group and averages coefficients.

• DFE: Traditional dynamic fixed effects with all coefficients pooled.

Value

An object of class "panel_ardl" containing:

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.

See Also

hausman_test, generate_panel_data

Examples

## Not run: 
# 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",
  estimator = "pmg"
)
summary(pmg_model)

## End(Not run)

Panel Nonlinear ARDL (Panel NARDL)

Description

Panel data estimation with asymmetric/nonlinear ARDL specification using PMG, MG, or DFE estimators.

Usage

pnardl(formula, data, id, time, p = 1, q = 1,
       estimator = c("pmg", "mg", "dfe"),
       threshold = 0,
       effect = c("individual", "time", "twoways"),
       bootstrap = FALSE, nboot = 500)

## S3 method for class 'pnardl'
print(x, ...)
## S3 method for class 'pnardl'
summary(object, ...)

Arguments

Details

The Panel NARDL model extends the Shin et al. (2014) NARDL framework to panel data settings. It allows for asymmetric short-run and long-run effects while controlling for cross-sectional heterogeneity.

Three estimators are available:

• PMG: Pooled Mean Group - constrains long-run coefficients to be homogeneous while allowing short-run heterogeneity

• MG: Mean Group - estimates separate models for each unit and averages coefficients

• DFE: Dynamic Fixed Effects - assumes all coefficients are homogeneous except fixed effects

Value

An object of class "pnardl" containing:

References

Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework.

Pesaran, M. H., Shin, Y., & Smith, R. P. (1999). Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association.

See Also

panel_ardl, qnardl, mtnardl

Examples

## Not run: 
# Generate panel data
data <- generate_panel_data(N = 20, T = 50)

# Panel NARDL with PMG estimator
result <- pnardl(
  y ~ x1 + x2,
  data = data,
  id = "id",
  time = "time",
  estimator = "pmg"
)
summary(result)

# Panel NARDL with MG estimator
result_mg <- pnardl(
  y ~ x1,
  data = data,
  id = "id",
  time = "time",
  estimator = "mg"
)

# Panel NARDL with bootstrap standard errors
result_boot <- pnardl(
  y ~ x1,
  data = data,
  id = "id",
  time = "time",
  bootstrap = TRUE,
  nboot = 200
)

## End(Not run)

PSS Asymptotic Critical Values

Description

Get Pesaran, Shin & Smith (2001) asymptotic critical values for bounds test.

Usage

pss_critical_values(k, case = 3, level = "5%")

Arguments

Details

Returns the I(0) and I(1) critical value bounds from the original Pesaran, Shin & Smith (2001) tables.

Case specifications:

• 1: No intercept, no trend

• 2: Restricted intercept, no trend

• 3: Unrestricted intercept, no trend (default)

• 4: Unrestricted intercept, restricted trend

• 5: Unrestricted intercept, unrestricted trend

Value

A list with:

References

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.

See Also

boot_ardl, fourier_bounds_test

Examples

# Get 5% critical values for 3 regressors, Case III
cv <- pss_critical_values(k = 3, case = 3, level = "5%")
cv$F_bounds  # I(0) and I(1) bounds for F-test
cv$t_bounds  # I(0) and I(1) bounds for t-test

Quantile Nonlinear ARDL (QNARDL)

Description

Estimate Quantile Nonlinear ARDL models combining distributional and asymmetric effects.

Usage

qnardl(formula, data, tau = c(0.25, 0.5, 0.75),
       p = 1, q = 1, decompose = NULL, trend = FALSE)

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

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

## S3 method for class 'qnardl'
plot(x, var = NULL, type = "long_run", ...)

Arguments

Details

This function implements the QNARDL model which extends the NARDL framework of Shin, Yu & Greenwood-Nimmo (2014) to a quantile regression setting.

The model allows for:

• Asymmetric effects: Positive and negative changes in X can have different impacts on Y

• Distributional heterogeneity: Effects can vary across quantiles of the conditional distribution

The partial sum decomposition separates each regressor into positive and negative components.

Value

An object of class "qnardl" containing:

References

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.

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.

See Also

asymmetry_test, dynamic_multipliers, generate_oil_data

Examples

## Not run: 
# Generate oil price data
data <- generate_oil_data(n = 200)

# Estimate QNARDL
model <- qnardl(
  gasoline ~ oil_price + exchange_rate,
  data = data,
  tau = c(0.1, 0.25, 0.5, 0.75, 0.9)
)
summary(model)
plot(model, var = "oil_price")

## End(Not run)

Rolling and Recursive ARDL (R-ARDL)

Description

Time-varying ARDL bounds test using rolling or recursive windows to detect structural changes in cointegration relationships.

Usage

rardl(formula, data, method = c("rolling", "recursive"),
      window = 50, min_obs = 40, p = 1, q = 1, case = 3,
      parallel = FALSE, ncores = 2)

## S3 method for class 'rardl'
print(x, ...)
## S3 method for class 'rardl'
summary(object, ...)
## S3 method for class 'rardl'
plot(x, type = c("F", "ec", "lr", "all"), ...)

Arguments

Details

The Rolling ARDL (R-ARDL) approach implements time-varying bounds testing to detect structural changes in cointegration relationships. Two methods are available:

• Rolling: Fixed-size window that moves through the sample

• Recursive: Expanding window starting from initial observations

This is useful for detecting:

• Time-varying cointegration relationships

• Structural breaks in long-run parameters

• Changes in error correction speed

Value

An object of class "rardl" containing:

References

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.

See Also

boot_ardl, aardl

Examples

## Not run: 
# Generate example data
data <- generate_ts_data(n = 300)

# Rolling ARDL with 60-observation window
roll_result <- rardl(y ~ x1 + x2, data = data, method = "rolling", window = 60)
plot(roll_result, type = "all")
summary(roll_result)

# Recursive ARDL
rec_result <- rardl(y ~ x1 + x2, data = data, method = "recursive", min_obs = 50)
plot(rec_result, type = "F")

## End(Not run)