# Outlier Detection Methods

Predictor offers three methods for detecting outliers, or significantly extreme values:

In each case, the difference is calculated between historical data points and values calculated by the various forecasting methods. These differences are called residuals. They can be positive or negative depending on whether the historical value is greater than or less than the smoothed value. Various statistics are then calculated on the residuals and these are used to identify and screen outliers.

A certain number of values must exist before the data fit can begin. If outliers occur at the beginning of the data, they are not detected.

 Note: Time-series data is typically treated differently from other data because of its dynamic nature, such as the pattern in the data. A time-series outlier need not be extreme with respect to the total range of the data variation but it is extreme relative to the variation locally.

## Mean and Standard Deviation Method

For this outlier detection method, the mean and standard deviation of the residuals are calculated and compared. If a value is a certain number of standard deviations away from the mean, that data point is identified as an outlier. The specified number of standard deviations is called the threshold. The default value is 3.

This method can fail to detect outliers because the outliers increase the standard deviation. The more extreme the outlier, the more the standard deviation is affected.

## Median and Median Absolute Deviation Method (MAD)

For this outlier detection method, the median of the residuals is calculated. Then, the difference is calculated between each historical value and this median. These differences are expressed as their absolute values, and a new median is calculated and multiplied by an empirically derived constant to yield the median absolute deviation (MAD). If a value is a certain number of MAD away from the median of the residuals, that value is classified as an outlier. The default threshold is 3 MAD.

This method is generally more effective than the mean and standard deviation method for detecting outliers, but it can be too aggressive in classifying values that are not really extremely different. Also, if more than 50% of the data points have the same value, MAD is computed to be 0, so any value different from the residual median is classified as an outlier.

## Median and Interquartile Deviation Method (IQD)

For this outlier detection method, the median of the residuals is calculated, along with the 25th percentile and the 75th percentile. The difference between the 25th and 75th percentile is the interquartile deviation (IQD). Then, the difference is calculated between each historical value and the residual median. If the historical value is a certain number of MAD away from the median of the residuals, that value is classified as an outlier. The default threshold is 2.22, which is equivalent to 3 standard deviations or MADs.

This method is somewhat susceptible to influence from extreme outliers, but less so than the mean and standard deviation method. Box plots are based on this approach. The median and interquartile deviation method can be used for both symmetric and asymmetric data.