Theil's U index of inequality: THEIL

Theil's $U$ inequality index (Theil 1961) is a measure of the degree to which one time series ($X_i$) differs from another ($Y_i$). The index is computed as

$$U = \frac {\sqrt{\frac{1}{n} \sum (X_i - Y_i)^2}} {\sqrt{\frac{1}{n} \sum X_i^2} + \sqrt{\frac{1}{n} \sum Y_i^2}}$$ (9)

The score returned by the THEIL this test is $1 - U$ for consistency; $U$ varies from 0 to 1 with 1 meaning maximum disagreement. Like DBK, it performs a point-by-point matching of the two time series; if the lengths of reference and actual data do not match, a warning is issued, and only the number of pairs corresponding to the length of the shortest one is used.