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.
Parameters: | method : string {‘breakvar’} or None
alternative : string, ‘increasing’, ‘decreasing’ or ‘two-sided’
use_f : boolean, optional
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Returns: | output : array
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Notes
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:
H(h) = \sum_{t=T-h+1}^T \tilde v_t^2 \Bigg / \sum_{t=d+1}^{d+1+h} \tilde v_t^2
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 [R99] for the above formula and discussion, as well as additional details.
TODO
References
[R99] | (1, 2) Harvey, Andrew C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press. |