Calculating an annual inflation rate from monthly data

Question

Let's say I have the following inflation data (for 11 months):

"2015-01" = 3.85 "2015-02" = 2.22 "2015-03" = 1.21 "2015-04" = 0.46 "2015-05" = 0.35 "2015-06" = 0.19 "2015-07" = 0.80 "2015-08" = 0.35 "2015-09" = 0.57 "2015-10" = 0.74 "2015-11" = 0.75

Then, how to calculate an annual inflation rate? Somehow I thought that it should something like that:

• divide data by 100 to get decimal values
• sum everything and divide by 11 to get an average monthly value
• add 1
• raise to 11th degree
• subtract 1.

That somehow results in something like 12.10%, which looks like the right answer but not exactly (the page with data says it's 12.05%).

So, am I right, and if no, then where's my mistake?

Answer 1

You don't want to average them, since the rates are compounded and thus multiplicative. In other words, if inflation was 10% one month and 10% the next month, then over the two months prices went up 1.1*1.1 = 1.21 = 21%.

What you should do is divide all the numbers by 100 and add one to all of them to get conversion factors (i.e., so that 0% inflation is converted to the number 1). Then multiply all of the numbers to get an overall conversion factor. To convert that back to a percentage, subtract 1 and then multiply it by 100. So for the first row of your table it would be 1.0385 * 1.0222 * 1.0121 * .... When I do this, the results agree with what is shown on the table.

Answer 2

The year-to-date is

(1.0385*1.0222*1.0121*1.0046*
   1.0035*1.0019*1.008*1.0035*
   1.0057*1.0074*1.0075) - 1 = 0.120454 = 12.05 %

For a projection of the annual rate take the geometric mean to find the average monthly rate, then compound it for the annual rate:-

gm = (1.0385*1.0222*1.0121*1.0046*
    1.0035*1.0019*1.008*1.0035*
    1.0057*1.0074*1.0075)^(1/11) = 1.01039

annual rate = gm^12 - 1 = 13.2 %