Calling forecast engine with BEST algorithm and forecast combining

This topic describes the techniques used to call the forecast engine with BEST algorithm and the Forecast Combining techniques enabled. The selected techniques are used to combine the resultant one-step ahead forecast and determine, if combining the forecasts provide an improved forecast accuracy.

When Classic Combining option is selected, these techniques are used:

  • Simple Mean: Calculates the mean of the forecasts
  • Trimmed Mean: Sorts the forecast’s value in ascending order, delete ‘x’ extreme values (at both ends) and calculate the mean. ‘x’ is defined by the trim factor.
  • Winsorized Mean: Sorts the forecast value, replaces the extreme values ‘x', (at both ends) with ‘x+1’ and calculate the mean. ‘x’ is defined by the Winsorized factor.
  • Weighted AIC: Calculates the weight for the first 'x' best AIC values.

These optional Multivariate Linear Regression (MLR) techniques can be applied to combine the forecasts:

  • MLR using stochastic gradient descent (SGD) and train-test methodolog:
    • Applied with randomization if ‘Machine Learning Full Dataset randomization’ is selected in the forecast engine
    • Applied without randomization if ‘Machine Learning Full Dataset’ is selected in the forecast engine
  • MLR using stochastic gradient descent (SGD) and the cross -validation methodology is applied if ‘Machine Learning Cross-Validation’ is selected in the forecast engine.

The MLR techniques calculate a set of weights (one for each forecast within a time period, that is, one for each algorithm) as follows:

  • Set up an initial set of weights and an intercept (an underlying level not related to any forecast).
  • Loop over all ‘epoch’ data points number of times as defined in the forecast engine parameter.
  • Recalculate the weight for each data point within each main loop using SGD. Consequently, the weight is adjusted by considering a percentage of the one-step ahead forecast multiplied by the observation. The percentage is determined by the learning rate as defined in the forecast engine parameter.
  • The order of the test or training data is randomized before calculating the weights, when randomization is requested (that is, random number seed = 0).
Note: Combining options are not mutually exclusive. All methods can be included for the forecast combining process.