## Changes From Yesterday

We can also transform the original time series X — {X1, X2,..., XN} into a new time series that indicates the increase or decrease in count from the previous time step, which in our example is a day. Let us define this new time series by Yt — Xt - Xt-1 as the changes from the previous day. We can then use a control chart algorithm on the Y time series to detect the onset of an outbreak.

Figures 14.8 and 14.9 graph the results of applying the "changes-from-yesterday'' transformation to the data from Figure 14.5.When we compare the control chart in Figure 14.5 to the "changes-from-yesterday'' algorithm in Figures 14.8 and 14.9, we notice that the control chart can be too insensitive to recent changes while the yesterday approach can be too easily influenced by recent changes. We would like an algorithm that is a happy medium between these two approaches, such

figure 14.6 The black line ("count") shows the data.The dark gray line ("predict") shows the historical mean value, and the light gray line ("upper") is the 2-sigma upper level. The dark bars on the top show the degree of alarm: the larger the bar, the more surprised is the control chart (formally, the height of a bar is proportional to the log of the reciprocal of the alarm level from Eq. 4). We see that the control chart only became very excited on Monday, September 27, 2004.

figure 14.6 The black line ("count") shows the data.The dark gray line ("predict") shows the historical mean value, and the light gray line ("upper") is the 2-sigma upper level. The dark bars on the top show the degree of alarm: the larger the bar, the more surprised is the control chart (formally, the height of a bar is proportional to the log of the reciprocal of the alarm level from Eq. 4). We see that the control chart only became very excited on Monday, September 27, 2004.

Bars show alarm levels; max = 10

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