# How to calculate inter-annual variation of inflation for a 3 month period

I have the monthly indexes taken from the National Institute of Statistics of my country (below), then I can calculate its inter-annual variation easily:

((index month year - index same month year - 1) / index same month year - 1) * 100

But my problem is that I want to compare this inter-annual variation against Financial Statements that show 3, 6, 9 and 12 months values. Then this inter-annual variation is useless because it shows the price variation only for a month and not for 3, 6, 9, 12 months period.

To solve this problem, should I calculate the cumulative inflation of 3, 6, 9 and 12 months of each year, then calculate de inter-annual variation of that cumulative inflation and finally be able to compare them to the Financial Statement inter-annual variation?

Is there any other way to do this more accurately ?

• By "inter-annual", do you mean something like June 2017 vs June 2018, or Sept 2017 vs June 2017? Jul 28, 2019 at 2:31

If I understand correctly: you are going to try to correct for high levels of monthly inflation in financial reports, to ensure you are not being fooled by changes due to inflation instead of firm performance. The problem is that you have monthly inflation data from the government (warning: governments have every incentive to massage numbers in their favored direction, so be careful not to assume the official numbers given are accurate, reliable, or even vaguely useful!), but the firms only report data every 3 months.

If I have understood the goal and purpose correctly, the accuracy of your resulting calculation will depend upon how much inflation varies between months, and how the financial results flow across the time period for the firm. For example, if the firm has all results established at the beginning of the 3 month period (thus no inflation occurred in those numbers compared to the prior month as it happened all on the first day), then there should be a different answer than if the firm had all results at the end of the period (and thus more inflation has occurred), or if the operations and inflation happened smoothly over the whole time period. It is also possible that the accounting methods are such that it would be better to use a time-lagged inflation rate (pre-purchasing behavior vs an "accrued when incurred" accounting method).

Without knowing the nature of the business it is hard to say which calculation method is more accurate or reasonable, and high-inflation can cause some odd-yet-rational behavior that can make people do some unusual things (buying things for future delivery before the prices have gone up, inflating currently demanded prices to cover future expected inflation, signing people up with soft contracts and then cancelling them because the prices have changed so much, refusing to sign longer term contracts at all because the prices are changing so much, changing labor rates and prices hourly/daily/weekly to account for the constantly shifting prices, etc.).

I would suggest running your calculations a few different ways:

1. Re-calculate the inflation rate, binning it to be cumulative 3-month inflation rates, then apply it to the financial reports (the method mentioned originally by the OP).
2. Dis-aggregate the financial reports, creating synthetic monthly reporting data by dividing the 3-month reports evenly by 3 (so January is assumed to be 1/3rd of whatever Jan-March was), then applying the monthly inflation rates to the financial reports.
3. Time-lagged: run one of the prior two methods to calculate inflation rates, but then apply it time-lagged - so inflation for months 1-3 are only applied to the financial results for months 4-6, etc. You may also want to reverse it and play with different time-lag lengths, but the wisdom of this depends upon the local conditions and nature of the business.

Run them each of these ways, and then decide overall, do the differences matter in any appreciable way for the cases you are considering? If it is not "material" - it would not change your decisions, regardless of how inflation/deflation were applied to the results - then you can worry less about these sorts of details and just go with whatever is more convenient to calculate/communicate.

If you would change your decision entirely depending on what method is used, and you don't have enough low-level detail or familiarity with the firm to decide what method is likely to be a more accurate reflection of on-the-ground reality, that suggests you need more information, or you must accept much lower confidence in your analysis.

• Thank you very much for your answer, BrianH. The business is the insurance industry. It has seasonality then the inter-annual variation rate (of the primes - sales - ) is often compared to the inter-annual variation rate of the inflation. I guess what you said is right, I should apply rates to financial reports to "carry" values to the third, sixth, nineth or twelfth month or maybe, i'll make a warning at the foot of the plot, saying the values "are not adjusted by inflation" (i don't know english terms for that). Thanks again! Aug 4, 2019 at 20:45