statsmodels.tsa.ardl.UECMResults.bounds_test#

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

Cointegration bounds test of Pesaran, Shin, and Smith

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

One of the cases covered in the PSS test.

cov_typestr, optional

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 OLS.fit.

  • ‘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

      correction.

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.

asymptoticbool, optional

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 regressors, excluding the dependent variable, so if more regressors are included then simulation is always used. The simulation computes the test statistic under an assumption that the residuals are homoskedastic.

nsimint, optional

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

rngint, array_like of int, numpy.random.Generator, or numpy.random.RandomState, optional

Random number generator or seed to use when simulating critical values. Must be provided if reproducible critical value and p-values are required when asymptotic is False. If rng is None, a new Generator is created using fresh entropy from the operating system. If rng is an int or array of ints, a new Generator is created, seeded with rng. If rng is already a Generator or RandomState instance, that instance is used.

seedint, array_like of int, numpy.random.Generator, or numpy.random.RandomState, optional

Deprecated since version 0.15: seed has been deprecated. In-line with SPEC-007, use rng for passing a random number generator or seed.

Returns:
BoundsTestResult

Named tuple containing statistic, critical_values, pvalue, null and alternative. The statistic is the F-type test statistic favored in PSS.

Notes

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.

Cases:

  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.

The asymptotic critical values and p-values are those of Pesaran, Shin and Smith (2001) for \(k\) long-run regressors. \(k\) is the number of variables in exog that are included in the model, and does not count the dependent variable, fixed regressors or deterministic terms. A variable in exog that is excluded from the model by setting its order to None is not counted.

Changed in version 0.15.1: The asymptotic critical values and p-values were previously looked up with \(k\) one too large, which made the p-values too small.

The fixed regressors and the seasonal terms of the model are included in the regression as additional controls. They are not part of the tested restriction, and the critical values do not depend on them. The constant and trend are always those implied by case, and the trend of the model is ignored. A model constructed using deterministic is not supported since the process cannot be combined with the deterministic terms of case without ambiguity, and a NotImplementedError is raised. Use trend, seasonal and fixed to specify the deterministic terms instead.

Changed in version 0.15.1: The fixed regressors and the seasonal terms of the model are included in the test. They were previously omitted. A model constructed using deterministic raises a NotImplementedError rather than ignoring the process.

References