Depression is one of the mood disorders, and the positive family history would place her at risk for developing a mood disorder. From the management perspective, if you adhere to the guidelines in Lynn Clark's book SOS Help for Parents you can't go wrong. And, irrespective of the mood disorder possibility, you still have to manage the behavior.
Is there a family history of mood disorder? The description is consistent with a juvenile-onset mood disorder, particularly because you are identifying a pattern of cycling. Now that in itself is a bit unusual for a young child but not unheard of. The implication of mood disorder is that pharmacological treatment might be called for.
Thank you so much for your quick response. As to the family history... on the maternal side there is a clear pattern of depression which has, and is being treated with medicine. ADD is also present. Many have had very strong food sensitivities, with one who displayed anger when eating certain foods. (The family has tried to see if there are foods which might be setting off our granddaughter's behavioral changes, but haven't seemed to find a correlation. Perhaps we need to be more vigilant in our record-keeping.) On the paternal side, there is a pattern of addictive personalities. None of these seem to imply a mood disorder though.
Our next step seems to be keeping a daily journal of her sleep, food intake, activities, and mood(s) over several months. Thank you again.