I received the following question by email:

I was wondering if mathematical relationships exist between monthly, quarterly, and annual growth rates (percentage changes). For time series data …
1) Is there a mathematical formula to know by how many months the Month-to-Month changes lead turns in this-month-to-the-same-month-one-year-ago changes (annual changes)?
2) Is there a mathematical formula to know by how many quarters the Quarter-to-Quarter changes lead turns in this-quarter-to-the-same-quarte …