Nonlinear ARDL (NARDL) Bounds Test
Nonlinear Autoregressive Distributed Lag Bounds Test · Also known as: NARDL, asymmetric ARDL, nonlinear bounds testing approach, NARDL bounds testing
The Nonlinear ARDL bounds test, developed by Shin, Yu, and Greenwood-Nimmo (2014), extends the linear ARDL framework to detect asymmetric long-run relationships in time series. By decomposing a regressor into positive and negative partial sums, NARDL simultaneously tests for cointegration and estimates separate long-run effects for increases and decreases — without requiring all variables to be integrated of the same order.
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When to use it
Use NARDL when you have moderate-length time series (roughly 30 or more observations) and economic theory or prior evidence suggests that positive and negative changes in a regressor may have different long-run effects on the outcome — for example, oil prices on inflation, exchange-rate depreciations versus appreciations on trade balances, or income increases versus decreases on consumption. NARDL is also appropriate when you are uncertain whether variables are I(0) or I(1), since the bounds test accommodates mixed integration orders. Do not use NARDL if variables contain I(2) components, if the sample is very short (fewer than ~30 observations after lag selection), or if asymmetry is theoretically implausible — in that case the simpler linear ARDL model is preferred.
Strengths & limitations
- Simultaneously tests for cointegration and estimates asymmetric long-run coefficients in one equation.
- Works with mixed I(0)/I(1) regressors, avoiding pre-unit-root classification of each variable.
- Produces interpretable long-run and short-run asymmetric multipliers with formal Wald tests for symmetry.
- Estimated by OLS on a single reduced-form equation, so inference is straightforward.
- Dynamic multiplier plots provide an intuitive visual of how positive and negative shocks propagate over time.
- Requires a sufficiently long sample; lag selection depletes degrees of freedom quickly in short series.
- Critical value bounds assume no I(2) variables; pre-testing with ADF or KPSS is still necessary to rule out I(2).
- Assumes a single-equation conditional model, which may be invalid if x is endogenous with respect to y.
- Partial sum decomposition imposes a specific form of asymmetry; nonlinearity of a different shape (e.g., threshold or smooth transition) is not captured.
Frequently asked
How is NARDL different from the standard ARDL bounds test?
Standard ARDL assumes symmetric adjustment: a positive and a negative shock of equal size produce effects of equal magnitude but opposite sign. NARDL replaces the single regressor with its positive and negative partial sums, allowing the long-run (and short-run) coefficients to differ across the direction of change. A Wald test then formally checks whether the two coefficients are equal.
What integration order do the variables need to be?
NARDL accommodates variables that are I(0) or I(1), or a mixture of both. Variables must not be I(2); if any variable is integrated of order two, the critical value bounds of Pesaran et al. (2001) are invalid. Run ADF or KPSS tests to confirm the absence of I(2) before proceeding.
How do I choose the lag lengths p and q?
Select the lag order that minimises an information criterion — AIC is common in small samples. Then check residuals for serial correlation (Breusch-Godfrey LM test) and structural stability (CUSUM and CUSUM-of-squares tests). If the sample is short, keep lags parsimonious to preserve degrees of freedom.
What does a significant bounds F-test tell me?
It indicates that a long-run level relationship (cointegration) exists among y, x⁺, and x⁻. It does not by itself confirm asymmetry — you still need to test H₀: L⁺ = L⁻ with a Wald test to determine whether the long-run effects of positive and negative shocks differ significantly.
Can NARDL handle more than one asymmetric regressor?
Yes. Each additional regressor suspected of asymmetric effects is also decomposed into positive and negative partial sums, and the model is augmented accordingly. However, adding more partial sum pairs consumes degrees of freedom rapidly, so a long sample is especially important when multiple asymmetric regressors are included.
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 (pp. 281-314). Springer. DOI: 10.1007/978-1-4899-8008-3_9 ↗
- 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. DOI: 10.1002/jae.616 ↗
How to cite this page
ScholarGate. (2026, June 3). Nonlinear Autoregressive Distributed Lag Bounds Test. ScholarGate. https://scholargate.app/en/econometrics/nonlinear-ardl-bounds-test
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