An additive outlier, also known as an extreme value or an anomaly, is an observation that is significantly different from other observations in a dataset. It is an outlier in a univariate dataset, where the value deviates so much from the rest of the values that it affects the overall mean or sum. Additive outliers are usually caused by errors in measurements or data entry and can badly affect statistical analyses. Identification of additive outliers is critical in many fields, including finance, health, and social sciences. 

Statistical models that are built assuming a normal distribution can be severely impacted by such outliers, making the analysis unreliable. Therefore, detection and handling of additive outliers play a crucial role in ensuring accurate and efficient statistical analyses. 

Methods To Identify Additive Outliers

One effective way to identify additive outliers is through graphical analysis, specifically box plots and scatter plots. Adding a box plot with a whisker that extends to the maximum or minimum value might help visualize these outliers better. An alternative approach is to calculate the standardized deviation from the mean and identify all values beyond a certain threshold as outliers. Once identified, there are various strategies to handle additive outliers, including trimming, winsorizing, or removing the affected observations. 

Nevertheless, handling additive outliers requires careful consideration of a dataset’s characteristics and the analysis objective, as handling them incorrectly may lead to loss of valuable information and inaccurate analysis results. 

Outliers are known as the shift in the level of a time series, without any corresponding explanation. The outliers are inconsistent with the rest of the observations in the series, but can affect the analysis, and thus, the forecasting capability of the time series model. The presence of an additive outlier does not affect any subsequent observations. An additive outlier patch occurs in the series when the series have subsequent additive outliers. It is also referred to as an abnormal value, present in the isolated place in the series.  Additive outlier is a term applied to an observation in a time series which is affected by a non-repetitive intervention such as a strike, a war, etc. Only the level of the particular observation is considered affected. 

In contrast, an innovational outlier is one which corresponds to an extraordinary shock at some point T(time), which also influences subsequent observations in the series. An additive outlier corresponds to an exogenous alteration in a single variable in the entire time series. The presence of external causes makes the additive outliers to be related to the isolated events, like impulse effects and errors in measurement. 

By Plotting Time Series Data

When the time series data is plotted, the additive outliers can be easily identified as an isolated spike in the data. It is also represented as the Type 1 outlier. It is generally problematic and must be detected and managed or removed, since it contains two consecutive residual values, namely before and after the value of the additive outlier. Additive outliers are also known to pose significant effects on the observed properties of the time series since they tend to influence the residual suspicion as well as supposition parameters within the model.