Nonlinear ARDL (NARDL) Model
Nonlinear Autoregressive Distributed Lag Model · Also known as: NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing the regressor into cumulative positive and negative partial sums, it tests whether increases and decreases in a variable exert different effects on the outcome — a feature especially relevant in financial and energy economics where positive and negative shocks rarely cancel out symmetrically.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
+15 more
When to use it
Use NARDL when you suspect that positive and negative changes in a regressor affect the outcome differently — common in energy prices, exchange rates, monetary policy, and commodity markets. It is appropriate for time series that are I(0), I(1), or mixed, but not I(2). The sample should be at least 40–50 observations to estimate a reliable error-correction term. Do not use NARDL when you have no theoretical or empirical reason to expect asymmetry; imposing a nonlinear specification on symmetric data inflates parameters and reduces efficiency. Avoid it with very short series (fewer than 40 observations) or when all variables are clearly I(2).
Strengths & limitations
- Detects and estimates asymmetric long-run and short-run effects within a single coherent framework.
- Inherits the ARDL bounds-test advantage: works with I(0) and I(1) regressors without requiring a pre-unit-root classification.
- Dynamic multipliers provide a visual, horizon-by-horizon picture of how positive and negative shocks propagate.
- OLS estimation keeps inference straightforward once the partial-sum decomposition is done.
- Handles structural features such as price rigidity and downward wage stickiness that linear models cannot capture.
- Decomposes each regressor into two series, roughly doubling the parameter count; efficiency drops quickly in short samples.
- Asymptotic critical value bounds from Pesaran et al. (2001) remain approximate for small T; use bootstrap bounds when T < 80.
- If the true relationship is symmetric, NARDL overfits and standard symmetric ARDL is preferred.
- The model applies to a single equation; it does not generalise joint multivariate dynamics the way a VAR or VECM does.
Frequently asked
How is NARDL different from the standard linear ARDL model?
Standard ARDL assumes that positive and negative changes in a regressor have equal and opposite effects. NARDL relaxes this by replacing each regressor with two partial-sum series — one for cumulative increases and one for cumulative decreases — so the model estimates a separate long-run coefficient for each direction of change.
Can I use NARDL with I(2) variables?
No. The bounds-test critical values derived by Pesaran, Shin, and Smith (2001) are valid only for I(0) and I(1) variables. If any series is I(2), the test statistic has a non-standard distribution and inference collapses. Pre-test all variables and drop or difference any I(2) series before estimation.
How do I choose the lag order in NARDL?
Use an information criterion such as AIC or BIC to select the lag lengths p and q for the differenced terms, subject to residuals passing a Breusch-Godfrey autocorrelation test. For short samples (T < 80) keep the maximum lag order modest — typically no more than 2 or 3 — to preserve degrees of freedom.
What are dynamic multipliers and why are they useful?
Dynamic multipliers trace the cumulative response of y at each horizon h following a unit positive or negative shock to x. Plotting them side by side reveals whether the adjustment paths differ in speed or magnitude, providing a richer picture of asymmetry than the long-run coefficients alone.
If the Wald test for long-run symmetry is not rejected, should I switch to linear ARDL?
Yes. If both long-run and short-run Wald tests fail to reject symmetry, the extra parameters in NARDL are unnecessary and the parsimonious linear ARDL is preferred. Apply NARDL when asymmetry is theoretically motivated and then confirm it statistically.
Sources
- Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in Honor of Peter Schmidt: Econometric Methods and Applications (pp. 281–314). Springer. link ↗
- 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. link ↗
How to cite this page
ScholarGate. (2026, June 3). Nonlinear Autoregressive Distributed Lag Model. ScholarGate. https://scholargate.app/en/econometrics/nonlinear-ardl
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- ARDL Bounds TestEconometrics↔ compare
- Engle-Granger Cointegration TestEconometrics↔ compare
- Granger Causality TestEconometrics↔ compare
- Quantile RegressionEconometrics↔ compare
- Vector Error Correction ModelEconometrics↔ compare