Robust Nonlinear Autoregressive Distributed Lag (Robust NARDL) Model
Robust Nonlinear Autoregressive Distributed Lag Model · Also known as: Robust Nonlinear ARDL, Outlier-Robust NARDL, Robust Asymmetric ARDL, R-NARDL
Robust NARDL marries the asymmetric cointegration framework of Shin, Yu, and Greenwood-Nimmo (2014) with outlier-resistant estimation. It decomposes a regressor into positive and negative partial sums, tests for asymmetric long-run relationships via a bounds test, and replaces the OLS criterion with an M- or MM-estimator to guard against leverage points and additive outliers common in macroeconomic and financial time series.
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When to use it
Use Robust NARDL when you suspect an asymmetric long-run relationship in time series data and the sample likely contains outliers, structural breaks, or data anomalies — common in commodity prices, exchange rates, energy markets, and macroeconomic series spanning crises. It is appropriate when the standard NARDL bounds test is sensitive to a few influential observations that distort OLS estimates. Do not use it as a substitute for explicit structural-break tests; if the series has known regime shifts, an asymmetric cointegration model with break dummies may be more transparent. Also avoid it with very short samples (below about 50 observations) where robust estimates lose efficiency.
Strengths & limitations
- Captures asymmetric (positive vs. negative) long-run relationships that OLS-ARDL and linear cointegration miss.
- Robust M- or MM-estimation reduces the influence of outliers, structural breaks, and data irregularities on long-run coefficient estimates.
- Retains the NARDL bounds-testing approach, so no pre-testing for integration order is strictly required — the model handles I(0) and I(1) regressors simultaneously.
- Dynamic multipliers provide an intuitive picture of how positive and negative shocks propagate over time.
- Applicable to small-to-moderate samples typical in macroeconomics and finance.
- Robust estimation adds computational complexity and requires selecting the loss function and tuning constant (e.g. Huber c = 1.345), which can affect results.
- Critical values for the robust bounds test are not universally tabulated; simulation or bootstrap inference is often needed.
- If outliers reflect genuine structural breaks rather than data errors, down-weighting them may discard economically important information.
- The partial-sum decomposition assumes a specific form of asymmetry (cumulative); threshold or smooth-transition models may be more appropriate for regime-based asymmetry.
Frequently asked
How is Robust NARDL different from standard NARDL?
Standard NARDL uses ordinary least squares to estimate the error-correction equation, making it vulnerable to outliers. Robust NARDL replaces OLS with an M- or MM-estimator that assigns lower weight to observations with large residuals, so the long-run asymmetric coefficients are driven by the majority of the data rather than a few extreme points.
Do I need to pre-test for unit roots before Robust NARDL?
The NARDL bounds-testing framework accommodates both I(0) and I(1) regressors, so strict unit-root pre-testing is not mandatory. However, you must ensure no variable is I(2); use robust unit-root tests (e.g. Zivot-Andrews or robust ADF variants) if the series contains potential outliers.
Which loss function should I use for the robust estimation step?
The Huber loss (tuning constant c ≈ 1.345 for 95% efficiency under normality) is a common default. For heavier contamination, the Tukey bisquare combined with an MM-estimator offers higher breakdown point. Report sensitivity to the choice of tuning constant.
How do I test for asymmetry in the Robust NARDL?
Apply a Wald test on the null hypothesis that the long-run positive coefficient equals the long-run negative coefficient (θ+ = θ−). A significant result supports asymmetry. Check both long-run and short-run asymmetry separately, as they need not coincide.
Can Robust NARDL handle structural breaks?
Robust estimation reduces the influence of isolated outliers but is not a full structural-break correction. If the series has known break dates, include dummy variables or use break-augmented bounds tests alongside the robust estimator.
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 ↗
- Autoregressive distributed lag. Wikipedia. link ↗
How to cite this page
ScholarGate. (2026, June 3). Robust Nonlinear Autoregressive Distributed Lag Model. ScholarGate. https://scholargate.app/en/econometrics/robust-nardl
Which method?
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