📂Statistical Analysis

Time Series Analysis of Additive Outliers

Buildup

The most noticeable point in the graph above is the huge outlier near February 2015. Such extreme values can have a detrimental effect on analysis. Luckily, it was just a brief, momentary outlier.

Definition ¹

Outliers that do not change the fluctuation of data itself are called additive outliers.

Practice

Such additive outliers can be intuitively found, or you can use the detectAO() function of the TSA package. The method is as follows:

1. Conduct time series analysis with the original data without considering additive outliers.
2. Insert the returned model itself into the detectAO() function. Then you get the following results.
3. The index with the largest absolute value of lambda is prioritized as a candidate. In the screenshot above, it is the 55th.
4. Reflect the additive outlier and analyze again. Repeat until satisfactory results are obtained.

Analysis incorporating additive outliers requires a dynamic regression model. The idea is simple. If you think the 69th data is an AO, create dummy data where only the 69th value is 1 and all the rest are 0, and then conduct regression analysis. This is theoretically analogous to a pure pulse function, and the code is not difficult either.

In fact, once the AO is reflected, not only the point of the AO but also the fitting in other places is improved.

Code

The following is an example code written in R. Since there wasn’t a suitable example, data was attached, but there’s no need to download it directly as the link is already in the code.