statsmodels.tsa.ardl.UECMResults.bounds_test¶
- 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
- Parameters
- case{1, 2, 3, 4, 5}
One of the cases covered in the PSS test.
- cov_type
str
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_kwds
dict
,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
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.
- nsim
int
Number of simulations to run when computing exact critical values. Only used if
asymptotic
isTrue
.- 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
isFalse
.
- Returns
BoundsTestResult
Named tuple containing
stat
,crit_vals
,p_values
,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:
No deterministic terms
Constant included in both the model and the test
Constant included in the model but not in the test
Constant and trend included in the model, only trend included in the test
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.
References
- *
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.