ARDL Bounds Test (Pesaran Bounds Test)
Also known as: Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)
The ARDL bounds test is an autoregressive distributed lag method that tests for a cointegrating (long-run level) relationship between time series, introduced by Pesaran, Shin and Smith in 2001. Unlike the Johansen procedure, it remains valid whether the variables are I(0), I(1) or a mix of the two, and it is more reliable than Johansen in small samples of roughly 30 to 80 observations.
Key highlights
- Valid for any mix of I(0) and I(1) variables, so you need not pre-classify every series as stationary or not.
- More reliable than the Johansen procedure in small samples (about 30 to 80 observations).
- Estimated as a single OLS error-correction equation, yielding both long-run and short-run coefficients at once.
Intuition
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How it works
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When to use it
Use the ARDL bounds test on time series when you suspect a long-run equilibrium relationship but the variables have mixed orders of integration. It needs at least about 30 observations and is especially valuable in small to moderate samples. The crucial requirement is that no variable is I(2): confirm the integration order with ADF or Phillips-Perron unit-root tests beforehand. The lag length should be selected with AIC or BIC, and the residuals must be free of autocorrelation, which a Breusch-Godfrey test verifies.
Strengths & limitations
- Valid for any mix of I(0) and I(1) variables, so you need not pre-classify every series as stationary or not.
- More reliable than the Johansen procedure in small samples (about 30 to 80 observations).
- Estimated as a single OLS error-correction equation, yielding both long-run and short-run coefficients at once.
- Breaks down if any variable is I(2); the bounds critical values are no longer valid.
- The test can return an inconclusive verdict when the F-statistic lands between the lower and upper bounds.
- Results are sensitive to the chosen lag length and require autocorrelation-free residuals to be trustworthy.
Common pitfalls
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Applications
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Frequently asked
How is the ARDL bounds test different from Johansen cointegration?
The Johansen procedure requires all variables to be integrated of the same order, typically I(1). The bounds test relaxes this: it works with any mix of I(0) and I(1) variables and is more reliable in small samples, which is why it is often preferred for short macroeconomic series.
What does an inconclusive result mean?
The test compares one F-statistic against a lower I(0) bound and an upper I(1) bound. If the statistic falls between them the outcome is inconclusive, meaning the data do not let you decide on cointegration without knowing the exact integration order of the variables.
Why must no variable be I(2)?
The Pesaran critical-value bounds are derived under the assumption that variables are I(0) or I(1). An I(2) variable violates that assumption, so the bounds no longer apply and the test is invalid. Always confirm the orders with ADF or Phillips-Perron tests first.
When should I use the Narayan (2005) critical values?
Use them in small samples, roughly 30 to 80 observations. The standard Pesaran bounds are asymptotic, so they can mislead with short series; Narayan computed finite-sample critical values that give more accurate decisions.
Sources
- 1.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.
- 2.Narayan, P. K. (2005). The Saving and Investment Nexus for China: Evidence from Cointegration Tests. Applied Economics, 37(17), 1979–1990.
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ScholarGate. (2026, June 1). ARDL Bounds Test. ScholarGate. https://scholargate.app/econometrics/ardl-bounds-test