UnobservedComponentsResults.test_heteroskedasticity(method, alternative='two-sided', use_f=True)
Test for heteroskedasticity of standardized residuals
Tests whether the sum-of-squares in the first third of the sample is significantly different than the sum-of-squares in the last third of the sample. Analogous to a Goldfeld-Quandt test. The null hypothesis is of no heteroskedasticity.
output – An array with
The null hypothesis is of no heteroskedasticity. That means different things depending on which alternative is selected:
For \(h = [T/3]\), the test statistic is:
where \(d\) is the number of periods in which the loglikelihood was burned in the parent model (usually corresponding to diffuse initialization).
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  for the above formula and discussion, as well as additional details.
|||Harvey, Andrew C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.|
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