Robust ARDL Bounds Test for Cointegration
Also known as: Robust ARDL, Robust bounds testing approach, Sam-McNown-Goh bounds test, Bootstrap ARDL bounds test
The Robust ARDL bounds test is an augmented version of the Pesaran-Shin-Smith (2001) ARDL bounds testing approach that resolves its two key weaknesses: size distortion under mixed integration orders and the degenerate-case problem. It introduces three separate test statistics — an overall F-test and two new Wald statistics for the dependent and independent variables — evaluated against bootstrap-generated critical values.
Key highlights
- Eliminates the degenerate-case problem of the original ARDL bounds test by using three complementary test statistics.
- Bootstrap critical values are sample-specific and do not rely on tabulated I(0)/I(1) bounds, giving better size control in small samples.
- Valid for regressors that are purely I(0), purely I(1), or a mixture — no pre-testing of integration orders required.
- Single-equation framework retains the ARDL advantage of estimating short-run and long-run dynamics simultaneously.
- Robust to moderate serial correlation and heteroscedasticity in the error term when bootstrap residuals are resampled appropriately.
Intuition
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How it works
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When to use it
Use the robust ARDL bounds test when you are working with a small-to-medium time series where variables may be a mixture of I(0) and I(1) — and especially when you cannot confirm integration orders confidently with unit-root tests. It is the preferred alternative to the standard PSS bounds test when you suspect degenerate cases (all I(0) or partial cointegration) or when your sample size is small enough to make asymptotic critical values unreliable. Do not use it as a substitute for the Johansen test when all series are clearly I(1) and you need to count multiple cointegrating vectors, as the robust ARDL framework remains a single-equation estimator.
Strengths & limitations
- Eliminates the degenerate-case problem of the original ARDL bounds test by using three complementary test statistics.
- Bootstrap critical values are sample-specific and do not rely on tabulated I(0)/I(1) bounds, giving better size control in small samples.
- Valid for regressors that are purely I(0), purely I(1), or a mixture — no pre-testing of integration orders required.
- Single-equation framework retains the ARDL advantage of estimating short-run and long-run dynamics simultaneously.
- Robust to moderate serial correlation and heteroscedasticity in the error term when bootstrap residuals are resampled appropriately.
- Requires a correctly specified lag structure; information criteria (AIC, BIC) must be used carefully to avoid over- or under-fitting.
- Single-equation design cannot identify more than one cointegrating relationship — use Johansen or VECM when multiple cointegrating vectors are expected.
- Bootstrap inference is computationally intensive relative to standard bounds testing and depends on the bootstrap scheme chosen.
- Performance deteriorates with very short time series (T < 30) or with highly persistent near-I(2) variables.
Common pitfalls
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Applications
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Frequently asked
How is the robust ARDL bounds test different from the standard PSS bounds test?
The standard Pesaran-Shin-Smith (2001) test uses a single F-statistic and tabulated bounds. The robust version adds two extra Wald statistics — one for the lagged dependent variable and one for the lagged regressors — and uses bootstrap critical values. This combination eliminates degenerate cases and improves size control in small samples.
Do I still need to run unit-root tests before the robust ARDL bounds test?
Not strictly. The test is valid for any mixture of I(0) and I(1) regressors. However, you should confirm that no variable is I(2) or higher, because the framework is not valid in that case. A simple ADF or KPSS test to rule out I(2) is advisable.
What does it mean if only one or two of the three statistics are significant?
Cointegration is confirmed only when all three statistics reject the null. If fewer than three reject, the result is inconclusive or indicates a degenerate case (e.g., all variables are I(0)), which requires further investigation rather than an outright conclusion of no cointegration.
How many bootstrap replications are typically used?
Sam et al. (2019) use 2,000 replications in their simulations. In practice, 1,000 to 5,000 replications strike a balance between precision and computation time, with larger numbers recommended when the sample is very small.
Can the robust ARDL bounds test handle structural breaks?
Not directly. Like the original ARDL bounds test, it assumes parameter stability over the sample. If structural breaks are suspected, you should either restrict the sample to the stable period or use a cointegration test that explicitly accounts for breaks, such as the Gregory-Hansen test.
Sources
- 1.Sam, C. Y., McNown, R., & Goh, S. K. (2019). An augmented autoregressive distributed lag bounds test for cointegration. Economic Modelling, 80, 130-141.
- 2.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.
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ScholarGate. (2026, June 3). Robust ARDL bounds test. ScholarGate. https://scholargate.app/econometrics/robust-ardl-bounds-test