statsmodels.tsa.statespace.exponential_smoothing.ExponentialSmoothingResults.test_heteroskedasticity¶

ExponentialSmoothingResults.
test_heteroskedasticity
(method, alternative='twosided', use_f=True)¶ Test for heteroskedasticity of standardized residuals
Tests whether the sumofsquares in the first third of the sample is significantly different than the sumofsquares in the last third of the sample. Analogous to a GoldfeldQuandt test. The null hypothesis is of no heteroskedasticity.
 Parameters
 method{‘breakvar’,
None
} The statistical test for heteroskedasticity. Must be ‘breakvar’ for test of a break in the variance. If None, an attempt is made to select an appropriate test.
 alternative
str
, ‘increasing’, ‘decreasing’ or ‘twosided’ This specifies the alternative for the pvalue calculation. Default is twosided.
 use_fbool,
optional
Whether or not to compare against the asymptotic distribution (chisquared) or the approximate smallsample distribution (F). Default is True (i.e. default is to compare against an F distribution).
 method{‘breakvar’,
 Returns
 output
ndarray
An array with (test_statistic, pvalue) for each endogenous variable. The array is then sized (k_endog, 2). If the method is called as het = res.test_heteroskedasticity(), then het[0] is an array of size 2 corresponding to the first endogenous variable, where het[0][0] is the test statistic, and het[0][1] is the pvalue.
 output
Notes
The null hypothesis is of no heteroskedasticity. That means different things depending on which alternative is selected:
Increasing: Null hypothesis is that the variance is not increasing throughout the sample; that the sumofsquares in the later subsample is not greater than the sumofsquares in the earlier subsample.
Decreasing: Null hypothesis is that the variance is not decreasing throughout the sample; that the sumofsquares in the earlier subsample is not greater than the sumofsquares in the later subsample.
Twosided: Null hypothesis is that the variance is not changing throughout the sample. Both that the sumofsquares in the earlier subsample is not greater than the sumofsquares in the later subsample and that the sumofsquares in the later subsample is not greater than the sumofsquares in the earlier subsample.
For \(h = [T/3]\), the test statistic is:
\[H(h) = \sum_{t=Th+1}^T \tilde v_t^2 \Bigg / \sum_{t=d+1}^{d+1+h} \tilde v_t^2\]where \(d\) = max(loglikelihood_burn, nobs_diffuse)` (usually corresponding to diffuse initialization under either the approximate or exact approach).
This statistic can be tested against an \(F(h,h)\) distribution. Alternatively, \(h H(h)\) is asymptotically distributed according to \(\chi_h^2\); this second test can be applied by passing asymptotic=True as an argument.
See section 5.4 of [1] for the above formula and discussion, as well as additional details.
TODO
Allow specification of \(h\)
References
 1
Harvey, Andrew C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.