QARDL

Flexibility is a core advantage: According to the
https://www.aptech.com/blog/the-quantile-autoregressive-distributed-lag-parameter-estimation-and-interpretation-in-gauss/: "One of the key advantages of the QARDL
model is that it can be used for data that is stationary, non-stationary, or a mixture of the two."

1. For cointegration analysis specifically: If your goal is to test for quantile cointegration (long-run relationships), then:
   • The variables should generally be nonstationary (I(1))
   • The traditional ARDL bounds testing framework (Pesaran, Shin, Smith 2001) does require the dependent variable to be I(1)
   • QARDL extends this framework to the quantile context
2. What the Cho, Kim, Shin (2015) paper establishes: The QARDL framework provides asymptotic theory for estimation with nonstationary regressors, allowing both
   short-run and long-run parameter estimation across quantiles.

Practical Guidance

Sources

• https://www.aptech.com/blog/the-quantile-autoregressive-distributed-lag-parameter-estimation-and-interpretation-in-gauss/
• https://www.sciencedirect.com/science/article/abs/pii/S0304407615001645
• https://github.com/aptech/gauss-qardl