UECMResults.bounds_test(case, cov_type='nonrobust', cov_kwds=None, use_t=True, asymptotic=True, nsim=100000, seed=None)[source]

Cointegration bounds test of Pesaran, Shin, and Smith

case{1, 2, 3, 4, 5}

One of the cases covered in the PSS test.


The covariance estimator to use. The asymptotic distribution of the PSS test has only been established in the homoskedastic case, which is the default.

The most common choices are listed below. Supports all covariance estimators that are available in

  • ‘nonrobust’ - The class OLS covariance estimator that assumes homoskedasticity.

  • ‘HC0’, ‘HC1’, ‘HC2’, ‘HC3’ - Variants of White’s (or Eiker-Huber-White) covariance estimator. HC0 is the standard implementation. The other make corrections to improve the finite sample performance of the heteroskedasticity robust covariance estimator.

  • ‘HAC’ - Heteroskedasticity-autocorrelation robust covariance estimation. Supports cov_kwds.

    • maxlags integer (required) : number of lags to use.

    • kernel callable or str (optional)kernel

      currently available kernels are [‘bartlett’, ‘uniform’], default is Bartlett.

    • use_correction bool (optional)If true, use small sample


cov_kwdsdict, optional

A dictionary of keyword arguments to pass to the covariance estimator. nonrobust and HC# do not support cov_kwds.

use_tbool, optional

A flag indicating that small-sample corrections should be applied to the covariance estimator.


Flag indicating whether to use asymptotic critical values which were computed by simulation (True, default) or to simulate a sample-size specific set of critical values. Tables are only available for up to 10 components in the cointegrating relationship, so if more variables are included then simulation is always used. The simulation computed the test statistic under and assumption that the residuals are homoskedastic.


Number of simulations to run when computing exact critical values. Only used if asymptotic is True.

seed{None, int, sequence[int], RandomState, Generator}, optional

Seed to use when simulating critical values. Must be provided if reproducible critical value and p-values are required when asymptotic is False.


Named tuple containing stat, crit_vals, p_values, null` and ``alternative. The statistic is the F-type test statistic favored in PSS.


The PSS bounds test has 5 cases which test the coefficients on the level terms in the model

\[\Delta Y_{t}=\delta_{0} + \delta_{1}t + Z_{t-1}\beta + \sum_{j=0}^{P}\Delta X_{t-j}\Gamma + \epsilon_{t}\]

where \(Z_{t-1}\) contains both \(Y_{t-1}\) and \(X_{t-1}\).

The cases determine which deterministic terms are included in the model and which are tested as part of the test.


  1. No deterministic terms

  2. Constant included in both the model and the test

  3. Constant included in the model but not in the test

  4. Constant and trend included in the model, only trend included in the test

  5. Constant and trend included in the model, neither included in the test

The test statistic is a Wald-type quadratic form test that all of the coefficients in \(\beta\) are 0 along with any included deterministic terms, which depends on the case. The statistic returned is an F-type test statistic which is the standard quadratic form test statistic divided by the number of restrictions.



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.