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I am using KPSS test to verify if my process has constant variance around the mean, but I am not sure if this is the correct test for my case. In KPSS the null hypothesis is that the process is stationary.

For example for two separate random variables, x, y:

from statsmodels.tsa.stattools import kpss

x = np.random.randn(100) # variance 1
y = np.random.randn(100)*10 # variance 100
z = np.concatenate([x,y]) # make one big vector of size 200

statistic, pvalue, lags, crit = kpss(z,'c')

print(pvalue)
out: 0.1

P value is 0.1 (or greater), so I can not reject the null. But clearly, the variance of first 100 observations is 1 and for the other 100 obserations it is 100. What test should I use?

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KPSS considers an alternative of a unit root to the null of no unit root. Heteroskedasticity is a different thing from a unit root. You should look for tests designed specifically to detect heteroskedasticity where the alternative is a heteroskedastic series to the null of a homoskedastic series.

For example, consider Levene's test, Bartlett's test, or the Brown–Forsythe test. In the simple case of comparing variances of two normal populations, an $F$-test of equality of variances will be appropriate. However, it is notoriously sensitive to the normality assumption.

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