Shifts in variance

The algorithm for detecting regime shifts in variance was originally introduced in Rodionov (2005b). Its application is based on the assumption that all regime shifts in mean are removed, that is, the values of the time series are deviations from the zero mean. When using STARS, it is recommended to run this test from the "ResM" worksheet. The same two parameters, the target significance level and the cutoff length, control the magnitude of the shifts and the length of the regimes to be detected. The Huber's tuning constant is used to reduce the weight of outliers. For details on regime shift detection in variance see Rodionov (2016).

An example of a regime shift in variance is presented in Fig. 1. It shows monthly values of the Arctic Oscillation index from January 1995 through July 2015. A statistically significant shift in the variance is detected in April 2009. The variance in the more recent period is doubled in comparison with the earlier period (1.67 vs. 0.81). The p-value for the difference is 0.0001.

Rodionov (2016) compared STARS with the Iterated Cumulative Sum of Squares (ICSS), one of the most popular methods for detecting change points in variance. In Monte Carlo experiments, STARS outperformed ICSS in the overwhelming majority of the modeled scenarios with different sequences of variance regimes. The STARS advantage was particularly apparent in the case of outliers in the series. On the other hand, STARS has more parameters to adjust than ICSS, which requires more experience from the user in order to select those parameters properly. Therefore, ICSS can serve as a good starting point of a regime shift analysis. The ICSS software is free for those who purchased STARS.

When tested on climatic time series, in most cases both methods detected the same change points in the longer series (252–787 monthly values). The only exception was the Arctic Ocean sea surface temperature (SST) series, when ICSS found one extra change point that appeared to be spurious. As for the shorter time series (66–136 yearly values), ICSS failed to detect any change points even when the variance doubled or tripled from one regime to another. For these time series, STARS is recommended.