BEST algorithm and forecast combining in forecast engine

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).