Shifts in mean

Click Shifts --> Shift Detection to open the entry form as in the figure below. The entire data range is automatically selected. You can select your own data range by clicking the button with underscore.

Entry form for calculating regime shifts.

There are two parameters that control the magnitude and scale of the regimes to be detected, the target significance level p, and the cut-off length l. The target significance level is the level at which the null hypothesis that the mean values of the two regimes are equal is tested using the two-tailed Student t-test. The lower the significance level, the larger the magnitude of the shift should be in order to be detected. The target significance level guarantees that the shifts between the regime of l years in length or longer detected by the method will be significant at least at this level. After all the regime shifts are detected, the program also calculates the actual significance levels for the shifts. In some rare circumstances when the regimes are shorter than l years,  but  the shifts between them are large enough to be detected, the actual significance level may be slightly higher than the target one.

The cut-off length is similar to the 100% cut-off point in filtering. The regimes that are longer than the cut-off length will all be detected. If the regimes are shorter than the cut-off length, the probability for them to be detected reduces proportionally to their length. Generally speaking, the shorter the cut-off length, the shorter the regimes that will be detected (and vice versa), but it's not always true. The reason is that the cut-off length also affects the critical magnitude of the shift between the regimes to be detected. For example, let's assume that the difference between the mean values of two regimes is statistically significant at the 0.01 level if the cut-off length is 10 years. But if the cut-off length is reduced to 5 years, the critical magnitude of the shift increases (for the same target significance level), and the regimes may not be detected. It is recommended to experiment with different significance levels and cut-off lengths to better understand their mutual effect on regime detection.

The program also requires the Huber's weight parameter that controls the weights assigned to the outliers (see below for more information). Therefore this parameter affects the average value of the regimes.

For each time series, the program calculates the regime shift index (RSI), the mean value of the regimes with equal and unequal weights, regime length, final confidence levels for the shifts and the weights of the outliers. This information for each variable is placed in a separate worksheet along with the corresponding graphs. The program also calculates the combined RSI ("Summary" worksheet) and residuals after the stepwise regime function is removed ("Residuals" worksheet). You can apply the method again to the residual worksheet, if you wish, but it has to be renamed first if the output is placed in the same workbook. The residuals can also be used to check for regime shift in the variance (no need to rename the worksheet in this case).