statsmodels.tsa.stattools.breakvar_heteroskedasticity_test¶
- statsmodels.tsa.stattools.breakvar_heteroskedasticity_test(resid, subset_length=0.3333333333333333, alternative='two-sided', use_f=True)[source]¶
Test for heteroskedasticity of residuals
Tests whether the sum-of-squares in the first subset of the sample is significantly different than the sum-of-squares in the last subset of the sample. Analogous to a Goldfeld-Quandt test. The null hypothesis is of no heteroskedasticity.
- Parameters:
- residarray_like
Residuals of a time series model. The shape is 1d (nobs,) or 2d (nobs, nvars).
- subset_length{
int
,float
} Length of the subsets to test (h in Notes below). If a float in 0 < subset_length < 1, it is interpreted as fraction. Default is 1/3.
- alternative
str
, ‘increasing’, ‘decreasing’ or ‘two-sided’ This specifies the alternative for the p-value calculation. Default is two-sided.
- use_fbool,
optional
Whether or not to compare against the asymptotic distribution (chi-squared) or the approximate small-sample distribution (F). Default is True (i.e. default is to compare against an F distribution).
- Returns:
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 sum-of-squares in the later subsample is not greater than the sum-of-squares in the earlier subsample.
- Decreasing: Null hypothesis is that the variance is not decreasing
throughout the sample; that the sum-of-squares in the earlier subsample is not greater than the sum-of-squares in the later subsample.
- Two-sided: Null hypothesis is that the variance is not changing
throughout the sample. Both that the sum-of-squares in the earlier subsample is not greater than the sum-of-squares in the later subsample and that the sum-of-squares in the later subsample is not greater than the sum-of-squares in the earlier subsample.
For \(h = [T/3]\), the test statistic is:
\[H(h) = \sum_{t=T-h+1}^T \tilde v_t^2 \Bigg / \sum_{t=1}^{h} \tilde v_t^2\]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 use_f=False as an argument.
See section 5.4 of [1] for the above formula and discussion, as well as additional details.
References
[1]Harvey, Andrew C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.