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It should be noted that the shift detection algorithm employed in STARS is quite robust to the presence of weak to moderate outliers, even if their weights are not reduced. This is especially true if the outliers are located away from the change points. Figure 1 shows a random time series of 60 data points (1901-1960) generated from a standard normal distribution with a shift from zero to one in 1931 and an outlier of 3.5 standard deviations in 1914. Even at h = 6, STARS correctly detects the change point in 1931.
Fig. 1. An example of robustness of STARS to outliers. An outlier in 1914 did not affect the detection of a regime shift in 1931.
It becomes more difficult to deal with outliers if they are located closer to the change point. This is illustrated in Figs. 2 and 3 featuring an outlier in 1927. If the weight of this outlier is not reduced (h = 6), STARS detects a shift in 1927 (Fig. 2). When the tuning constant is reduced to h = 2, thus decreasing the weight of the outlier, STARS correctly identifies a shift in 1931 (Fig. 3). Based on just a visual inspection of the time series in this example, it is difficult to decide whether the data point in 1927 is an error or a legitimate observation, marking the beginning of a new regime, where it is less of an outlier. In any case, this data point deserves a special attention, and the researcher should use his/her own judgement about the underlying process, and weather to reduce the weight of the outlier or leave it intact.
Fig. 2. An outlier in 1927 changes the regime shift from 1931 to 1927.
Fig. 3. Using h = 2 reduces the weight of the outlier in 1927 and enables a correct detection of the shift in 1931.
Another example illustrating the negative effect of outliers on detection of change points is presented in Fig. 4. In this time series with a predefined regime shift upward in 1931, an outlier with a negative sign was inserted in 1937. Due to this outlier, a regime shift was detected only in 1938. Again, using the tuning constant of h = 2 enables a correct detection of the regime shift in 1931 (Fig. 5).
Fig. 4. An example of a delayed shift detection due to an outlier in the second regime.
Fig. 5. The effect of the outlier in 1937 is reduced using the tuning constant of h = 2. The regime shift in 1931 is detected correctly.
To quickly identify possible outliers, it is recommended to use a smaller tuning constant first, for example h = 2, and then decide how to treat those outliers depending on their nature. Overall, h = 2 provides stable results in most cases, and hence, is used as a default value.
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