Removing Outliers

What is an Outlier

It is a historical data point which is overly high or low compared to the other historical points.  These are often caused by a one time order event that results in a significant spike in demand. The removal is based on a normal distribution of demand.

Outliers are removed to the bottom and upper levels when running a middle out forecast. For top down, outliers are only removed at the forecasting level.

When are Outlier Applied

Where applicable

  • Croston Models
    • Croston Standard
    • Croston SB (Syntethos Boylan)
  • Exponential Smoothing Models
    • Single Exponential Smoothing
    • Double Exponential Smoothing
    • Triple Exponential Smoothing

Where not applicable

  • Bootstrapping (used for lumpy demand)
  • Simple moving average (used when no recent demand)
  • Last 13 weeks average (used to take into account only recent sales and produce accurate result based on them)
  • Negative historical values


  1. The best fit forecasting model is applied against the time series, the residuals (fitted errors) are generated and their standard deviation is calculated.
  2. If the size of the largest error exceeds the outlier threshold, the point is flagged as an outlier and the historic value for the period is replaced with the fitted value.
  3. The procedure is then repeated using the corrected history for as many iterations as defined in system settings. This is done until either no outliers are detected or the specified maximum number of iterations is reached.
  4. You can adjust the Sigma Threshold setting to make the outlier threshold more or less sensitive. The default setting is 3 standard deviation. The higher the number fewer outliers are removed.
  5. Maximum iterations allows you to set the maximum number of iterations permitted during outlier detection for a given item. This setting thereby also defines the maximum number of outliers than can be detected for a given item. This is user defined. Each iteration is another standard deviation.


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