<p>Let’s assume that the price index is denoted <span class="math-container">$p_t$</span>, with <span class="math-container">$p_1$</span> the first month, and <span class="math-container">$p_4$</span> the fourth. To calculate the 3-month annualised rate between the 1st and 4th month, we note that :
<span class="math-container">$p_4 = (1 + r)^{\frac{1}{4}} p_1,$</span> where <span class="math-container">$r$</span> is the annualised inflation rate. </p>

<p>Or: <span class="math-container">$(1+r) = (\frac{p_4}{p_1})^4$</span>.</p>

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

CC BY-SA 4.0
2019-04-12T19:38:41.683Z
2019-04-12T19:38:41.683Z
Brian Romanchuk
<p>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.</p>

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

<p><a href="https://i.sstatic.net/0QkOI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/0QkOI.png" alt="enter image description here"></a></p>

<p>From which is has been calculated that the 3m annualised rate is as follows:</p>

<p><a href="https://i.sstatic.net/gtRGY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/gtRGY.png" alt="enter image description here"></a></p>

<p>How is this number calculated on a rolling basis?</p>

CC BY-SA 4.0
2019-04-10T11:08:58.087Z
You can’t do it from YoY rates; you need the underlying index.
Brian Romanchuk
CC BY-SA 4.0
2019-04-12T08:16:24.073Z
@BrianRomanchuk If you had MoM rates e.g. 0.7% 0.3% 0.4% how should it be calculated then?
andre1990
CC BY-SA 4.0
2019-04-12T19:27:36.327Z
Convert the three monthly rates to (1+r) form, then multiply the 3 terms, and you get (1 + r_3m). To annualize, take to the power 4.
Brian Romanchuk
CC BY-SA 4.0
2019-04-12T19:29:37.837Z
(In the previous, I assume that the monthly rate is not annualised.)
Brian Romanchuk
<inflation>
Calculating 3m annualised rates
andre1990
# Calculating 3m annualised rates

(Asked by: username_0 on 2019-04-10)

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:

[![enter image description here](https://i.sstatic.net/0QkOI.png)](https://i.sstatic.net/0QkOI.png)

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

[![enter image description here](https://i.sstatic.net/gtRGY.png)](https://i.sstatic.net/gtRGY.png)

How is this number calculated on a rolling basis?

**Tags:** inflation
> **Comments:**
> **username_1**: You can’t do it from YoY rates; you need the underlying index.  
> **username_0**: @BrianRomanchuk If you had MoM rates e.g. 0.7% 0.3% 0.4% how should it be calculated then?  
> **username_1**: Convert the three monthly rates to (1+r) form, then multiply the 3 terms, and you get (1 + r_3m). To annualize, take to the power 4.  
> **username_1**: (In the previous, I assume that the monthly rate is not annualised.)  

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## 1 answers

### Answer by username_1 on 2019-04-12. Score: 1

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.


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