Calculating 3m annualised rates Calculating 3m annualised rates is a concept I've been struggling with for some time, but I think the below example illustrates what I am looking at trying to understand.

The past 6 months of monthly YoY inflation data for Hungary has been as follows:



From which is has been calculated that the 3m annualised rate is as follows:



How is this number calculated on a rolling basis?
Let’s assume that the price index is denoted $p_t$, with $p_1$ the first month, and $p_4$ the fourth. To calculate the 3-month annualised rate between the 1st and 4th month, we note that :
$p_4 = (1 + r)^{\frac{1}{4}} p_1,$ where $r$ is the annualised inflation rate. 

Or: $(1+r) = (\frac{p_4}{p_1})^4$.

We cannot calculate the price index level from the 12-month change data; you need either index levels or 1-month percentage changes.