Bayesian NARDL: Nonlinear ARDL with Bayesian Estimation
Bayesian Nonlinear Autoregressive Distributed Lag Model · Also known as: Bayesian NARDL, Bayesian nonlinear ARDL, Bayesian asymmetric ARDL, B-NARDL
Bayesian NARDL combines the Nonlinear Autoregressive Distributed Lag framework of Shin, Yu, and Greenwood-Nimmo (2014) with Bayesian posterior inference. It models asymmetric long-run cointegration — allowing positive and negative shocks to a regressor to have different equilibrium effects — while incorporating prior knowledge and producing full posterior distributions over all parameters, including the asymmetry gap.
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When to use it
Use Bayesian NARDL when your economic or financial time series plausibly exhibit asymmetric long-run adjustment — for example, oil prices, exchange rates, or commodity prices that respond differently to booms than to busts — and when you want to incorporate prior information or obtain full posterior inference rather than point estimates. It is especially useful with short series (T < 80) where classical NARDL estimates are unstable, or when you wish to propagate parameter uncertainty into forecasts. Do not use it when the relationship is theoretically symmetric and there is no substantive reason to model separate directional effects, or when the series are too short (T < 40) to identify the lag structure at all. The method requires careful prior elicitation; uninformative priors can still impose implicit regularisation that should be justified.
Strengths & limitations
- Captures asymmetric long-run cointegration: positive and negative shocks can have different equilibrium effects.
- Full posterior distributions over all parameters, including asymmetry contrasts, allow principled uncertainty quantification.
- Prior information from theory or previous studies can be formally incorporated, stabilising estimates for short or noisy series.
- Bayesian model comparison (Bayes factors, WAIC) provides a coherent framework for comparing symmetric ARDL against asymmetric NARDL specifications.
- Dynamic multipliers can be traced with posterior credible bands, giving richer impulse-response analysis than classical point estimates.
- Computationally intensive when MCMC is required; tractability depends on prior choice and series length.
- Prior elicitation is non-trivial: poorly specified priors can dominate the likelihood and bias posterior inference toward unrealistic asymmetry.
- Lag order selection must be carried out before or jointly with estimation; misspecification of the lag structure propagates into all posterior summaries.
- Results are sensitive to whether the partial-sum decomposition is justified by the data; applying NARDL to inherently symmetric processes inflates model complexity for no gain.
- Software support is more limited than for classical NARDL; researchers typically code MCMC samplers in R or Python rather than relying on turnkey routines.
Frequently asked
How does Bayesian NARDL differ from classical NARDL?
Classical NARDL uses OLS to estimate the error-correction form and relies on asymptotic Wald tests for asymmetry and bounds tests for cointegration. Bayesian NARDL places prior distributions on all parameters and uses the posterior to quantify uncertainty; this is especially valuable in short samples where classical t and F statistics have poor size and power.
What prior should I use for the long-run multipliers?
A weakly informative Normal prior centred on zero with moderate variance is a common starting point when no strong theoretical expectation exists. If theory implies a positive long-run elasticity, a prior that assigns most mass to positive values is appropriate. Always conduct a prior-sensitivity analysis by re-running the model with different prior scales.
Do I still need the bounds test in Bayesian NARDL?
Bayesian model comparison — comparing a model with vs. without the level terms using Bayes factors or WAIC — replaces the frequentist bounds test for cointegration. Some researchers run both as a robustness check.
Can Bayesian NARDL handle structural breaks?
Yes, with extensions: a Bayesian NARDL with time-varying parameters (state-space form) or mixture priors can accommodate parameter shifts. Alternatively, dummy variables for known break dates can be incorporated into the prior design.
How many observations do I need?
As a practical guideline, at least 60 observations are needed to estimate the lag structure reliably, though Bayesian shrinkage priors can help stabilise the model with as few as 40 observations. Fewer than 40 observations make asymmetry identification very difficult regardless of the estimation approach.
Sources
- Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In W. C. Horrace & R. C. Sickles (Eds.), Festschrift in Honor of Peter Schmidt: Econometric Methods and Applications (pp. 281–314). Springer. link ↗
- Koop, G. (2003). Bayesian Econometrics. Wiley. ISBN: 978-0470845677
How to cite this page
ScholarGate. (2026, June 3). Bayesian Nonlinear Autoregressive Distributed Lag Model. ScholarGate. https://scholargate.app/en/econometrics/bayesian-nardl
Which method?
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