## 312: Retroactive

The retroactive calculation option fits a CCA, PCR, or MLR model to an initial subset of the training period that must be specified. The initial subset consists of the first few years of the training period. The default is to use the first half of the full training period, but the user may wish to define a more appropriate initial training period. The shorter the initial training period is, the more years are available for producing retroactive forecasts, and the more reliable the performance measures are likely to be. However, if the initial training period is made too short, sampling errors in constructing the models may result in inaccurate retroactive forecasts.

After fitting a model to the initial training period, cross-validated forecasts are made for each year in this initial
shortened training period, and retroactive forecasts are then produced for the next
*
k
*
years, where
*
k
*
is the
model update interval. The model is then refitted using the initial training period plus these first
*
k
*
years, a new set
of cross-validated predictions is made, and retroactive forecasts are made for the following
*
k
*
years. This procedure is
repeated until the last year of the full training period is forecast. These forecasts are produced deterministically and
probabilistically. The probabilistic forecasts are calculated based on the error variance of the most recently available
cross-validated predictions.

The retroactive procedure then fits a model using the full training period, and cross-validates this model. These cross-validated forecasts are identical to those that are obtained using the cross-validated option. The cross-validated and the retroactive forecasts are available for performance analyses, and can be saved to an output file. (Note that only the cross-validated predictions for the entire training period are available: the preliminary cross-validated predictions for the shortened training periods are not retained.)

If the model is to be optimised, by identifying the best numbers of X, Y, and/or CCA modes, an optimal model is identified each time the retroactive model is updated. As a result, the retroactive option with optimisation may take a while to compute all the forecasts, especially if the model update interval is short.