Hi Abdur, our description of the Anthocyanin Reflectance Index was taken from this website, which cites the original articles by Gitelson, Chivkunova, and Merzlyak. We found the information we were looking for in their freely available article from 2009.
The original ARI index, (1/R550)-(1/R700), has a wide range of values, theoretically unlimited. However, it should be only used for vegetation, since the anthocyanins are substances present in higher plant leaves.
If you examine only the values of ARI in forested areas, you will notice the values aggregating around 0 - 0.1. However, if you would take into account non-forested areas, such as lakes or barren rock, the values skyrocket to between mostly, but not exclusively, -30 and 30. This however, would not be a correct use of the index.
On page 1867 of the article , you can see the resulting graph displaying ARI index ranging from 0 to 0.2. This is due to the fact that all the ARI values of the examined trees were in that range. Had the authors considered a wider range of tree species, these values might differ.
In summary, ARI is not limited to values of 0 to 0.2, however, most ARI values for trees, which is what the index is intended for, do appear to be in this range.