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Goodness Index

The Goodness Index menu permits the user to change the correlation coefficient use to calculate the index. Since version 11 the default coefficient has been Kendall's correlation, but in prior versions Pearson's correlation was used. Kendall's correlation is set as the default because CPT then attempts to maximise the discriminatory power of the forecasts and is insensitive to the distribution of the data. However, if it is considered important to minimise the squared errors in the forecasts then Pearson's correlation may be a preferred option. Note that selecting Pearson's correlation when the Transform Y Data is on can result in Pearson's skill scores that are noticeably poorer than the goodness index might suggest, and is not generally to be recommended.

The goodness of fit index can be interpreted as the average correlation between the cross-validated forecasts and observations for all series. (If the Transform Y Data is on then the cross-validated correlation is between the transformed forecasts and observations.) However, if the Pearson's or Spearman's correlation coefficient is used, rather than simply calculating an arithmetic average of the correlations, the correlations are first transformed to the Fisher z-scale, averaged, and then transformed back to the correlation scale (except in the case where any of the correlations are +/-1.0, in which case a simple average is calculated). The Fisher z-scale transform is used for Pearson's and Spearman's correlations because an average of these coefficients does not necessarily have an equivalent interpretation to the coefficient for an individual series.


 
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