Nonlinear Autoregressive Distributed Lag (NARDL) Model
Also known as: nonlinear ARDL, asymmetric ARDL, Doğrusal Olmayan ARDL (NARDL)
The NARDL model, introduced by Shin, Yu and Greenwood-Nimmo in 2014, extends the ARDL framework to capture asymmetric long-run and short-run relationships, testing whether positive and negative changes in a regressor affect the dependent variable differently.
Key highlights
- Captures asymmetric long-run and short-run effects that a linear ARDL would miss.
- Tests positive versus negative responses formally with a Wald symmetry test.
- Accommodates regressors that are a mix of I(0) and I(1) and visualises shock responses through dynamic multipliers.
Intuition
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How it works
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When to use it
Use NARDL for time-series data where you suspect that increases and decreases in an explanatory variable move the outcome by different amounts, in either the short or the long run. It needs a reasonable series length (at least about 50 observations) and requires that no variable is integrated of order two (I(2)); the variables may be a mix of I(0) and I(1). Always test the symmetry restrictions with a Wald test, visualise the shock response with dynamic multipliers, and check the residuals for autocorrelation and heteroscedasticity.
Strengths & limitations
- Captures asymmetric long-run and short-run effects that a linear ARDL would miss.
- Tests positive versus negative responses formally with a Wald symmetry test.
- Accommodates regressors that are a mix of I(0) and I(1) and visualises shock responses through dynamic multipliers.
- Requires a reasonably long series (at least about 50 observations) and breaks down if any variable is I(2).
- The partial-sum decomposition doubles the number of regressors, so the model is data-hungry and harder to interpret.
- Inference still depends on well-behaved residuals — autocorrelation or heteroscedasticity undermines the bounds test.
Common pitfalls
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Applications
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Frequently asked
How is NARDL different from a standard ARDL model?
Standard ARDL assumes a single symmetric relationship: a one-unit rise and a one-unit fall in a regressor have equal and opposite effects. NARDL splits each regressor into cumulative positive and negative changes and gives them separate coefficients, so increases and decreases can affect the outcome by different amounts in the short and long run.
What does the Wald test do in NARDL?
The Wald test checks the symmetry restrictions — whether the long-run coefficients on the positive and negative partial sums are equal, and separately whether the short-run dynamics are symmetric. Rejecting symmetry is the formal evidence that an asymmetric (nonlinear) specification is warranted.
Can I include I(2) variables in NARDL?
No. Like the underlying ARDL bounds-testing approach, NARDL requires that no variable is integrated of order two. The variables may be I(0), I(1), or a mixture, but an I(2) series invalidates the bounds test.
Why are dynamic multipliers important?
Dynamic multipliers trace how the dependent variable adjusts over time to a positive versus a negative unit shock in a regressor. They make the asymmetry visible — showing the differing speed and magnitude of adjustment that the coefficients only summarise.
Sources
- 1.Shin, Y., Yu, B. & Greenwood-Nimmo, M. (2014). Modelling Asymmetric Cointegration and Dynamic Multipliers in a Nonlinear ARDL Framework. In: Sickles, R. & Horrace, W. (Eds.), Festschrift in Honor of Peter Schmidt. Springer.
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Cite this page
ScholarGate. (2026, June 1). NARDL Model. ScholarGate. https://scholargate.app/econometrics/nardl-model