HomeTechniques and TipsCorrelation in @RISKCorrelated Time Series in Batch Fit

# 5.19. Correlated Time Series in Batch Fit

Applies to: @RISK 6.x/7.x

Can you tell me more about the correlation matrix shown in the fit summary after a time series batch fit? The coefficients in that matrix don't seem to match the results of Excel's CORREL( ) function; where do the numbers come from? How are they used?

The correlation matrix in the fit summary is the Spearman(*) correlations of the transformed historical data. Those transformed data are not available as numbers. However, you can see the graph of the transformed data by doing a single fit rather than a batch fit, and using the same transformations.

(*)The correlation matrix was Pearson in @RISK 6.0, but was changed to Spearman (rank order) in 6.1. When distributions with very different shapes are correlated, results with Pearson can be unsatisfactory. The change to the distribution-free Spearman rank order correlation was made for this reason, and to be consistent with how other correlations work in @RISK.

That correlation matrix in turn is used to correlate the projected distributions of the time series in each time period by the rank order method. The correlation is not applied to the numbers that you can see in a worksheet; it is the "raw" time series functions that are correlated.

Conceptual summary of a batch fit:

1. @RISK applies transforms to the historical data and then fits the transformed data. The transforms can be user selected, or if you click Auto Detect then @RISK will determine the transforms to apply.

@RISK computes the actual Spearman correlations of the transformed historical data. This is the matrix shown in the fit summary.

2. For projections, @RISK applies the projection functions shown in the worksheet cells. This is conceptually a two-stage process: first "raw" numbers are developed, projecting from the transformed historical data according to the fit. Then the "raw" numbers are de-transformed by reversing the transforms that were applied to the historical data, and the de-transformed projections become the final output of the functions that you see in the worksheet cells..

The correlation matrix is applied to the "raw" numbers, not to the final de-transformed projections that appear in the worksheet.

Last edited: 2015-06-23 