qardlr: Quantile Autoregressive Distributed Lag Model

R implementation of the Quantile Autoregressive Distributed Lag (QARDL) model by Cho, Kim & Shin (2015).

Overview

The qardlr package provides tools for estimating quantile-specific long-run equilibrium relationships and short-run dynamics using the QARDL framework. This approach extends classical ARDL cointegration analysis to the quantile regression setting, allowing researchers to examine how relationships vary across different points of the conditional distribution.

Installation

# Install from CRAN (when available)
install.packages("qardlr")

Key Features

Quantile regression across multiple tau values
BIC-based automatic lag selection (p, q)
Error Correction Model (ECM) parameterization
Long-run (β), short-run AR (φ), and impact (γ) parameters
Wald tests for parameter constancy across quantiles
Rolling/recursive QARDL estimation for stability analysis
Monte Carlo simulation for finite-sample properties
Publication-ready output tables (text, LaTeX, HTML)

Quick Start

library(qardlr)

# Load example data
data(qardl_sim)

# Basic QARDL estimation with automatic lag selection
fit <- qardl(y ~ x1 + x2, data = qardl_sim, 
             tau = c(0.25, 0.50, 0.75))

# View results
summary(fit)

# Wald tests for parameter constancy
wald_results <- qardl_wald(fit)
print(wald_results)

# Generate publication-ready table
cat(qardl_table(fit, type = "latex"))

The QARDL Model

The QARDL(p,q) model is specified as:

\[Q_{y_t}(\tau | \mathcal{F}_{t-1}) = c(\tau) + \sum_{i=1}^{p} \phi_i(\tau) y_{t-i} + \sum_{j=0}^{q-1} \gamma'_j(\tau) x_{t-j}\]

Key Parameters: - β(τ): Long-run parameters = Σγ(τ) / (1 - Σφ(τ)) - φ(τ): Short-run AR coefficients - γ(τ): Short-run impact parameters - ρ(τ): Speed of adjustment (ECM) = Σφ(τ) - 1

Functions

Function	Description
`qardl()`	Main QARDL estimation
`qardl_wald()`	Wald tests for parameter constancy
`qardl_rolling()`	Rolling/recursive window estimation
`qardl_simulate()`	Monte Carlo simulation
`qardl_bic_select()`	BIC-based lag selection
`qardl_table()`	Publication-ready tables

ECM Parameterization

Use ecm = TRUE for Error Correction Model form:

fit_ecm <- qardl(y ~ x1 + x2, data = qardl_sim, 
                 tau = c(0.25, 0.50, 0.75), 
                 ecm = TRUE)
summary(fit_ecm)

Rolling Window Analysis

# Rolling QARDL with 50-observation window
roll <- qardl_rolling(y ~ x1 + x2, data = qardl_sim,
                      tau = c(0.25, 0.50, 0.75), 
                      p = 2, q = 2, window = 50)
plot(roll, which = "beta", var = 1)

Monte Carlo Simulation

# Assess finite-sample properties
mc <- qardl_simulate(nobs = 200, reps = 1000, 
                     tau = c(0.25, 0.50, 0.75),
                     p = 1, q = 1, k = 1)
print(mc)

Citation

If you use this package, please cite:

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. https://doi.org/10.1016/j.jeconom.2015.01.003

Author

Dr. Merwan Roudane
Email: merwanroudane920@gmail.com

License

GPL-3