The changes in time series (and also in data series) can be checked by the Chow breakpoint test.
We split the series in two or more sub-series, and we compute the variances considering first only one expectation (for entire series), and an expectation for each sub-series. Of course, in the second case the variance is small.
We compute the number of degrees of freedom as the difference between the length of the series and the number of parameters, and next we compute the sum in the second case.
We compute the ratios between the sum of squares and the corresponding number of degrees of freedom, and finally the ratio of the obtained ratios. This value has the Snedecor-Fisher distribution (or F distribution), that has to be compared by the quantiles from statistical tables.
In the case of ARMA and ARIMA time series, we consider the obtained white noises, which have the expectation equal to zero. The differences between the sub-series and the entire series is on the magnitude of the white noises.