I have yearly sales forecast and constant seasonality (% of yearly sales). How can I come up with a seasonality that smooths the monthly growth?

Question

Let's say I have a yearly sales forecast (in $), such as {100,300,400,500}

I also have a monthly seasonality percentage (as % of total yearly sales), such as {5%,5%,15%,15%,10%,5%,10%,5%,10%,5%,10%,5%).

If I multiply December's percentage over Year 1, I would get the number 5, as 5%*100=5.

Yet, If I multiply January's percentage over Year 2, I would get the number 15, as 5%*300=15.

Although being correct in terms of %, such monthly growth rate is rather unusual.

How can I adapt the seasonality percentage to avoid unusual steps in a monthly sales forecast? I've tried to weight a CAGR growth but that didn't work.

As an answer, I would have a single seasonality percentage vector that would smooth out the monthly growth across 5 different years.

Thank you very much.

Answer 1

Any staisfactory response would be at least empirical, at least to deal with the point that you have a strong trend on top of your stated seasonality.

In particular, do the $5\%$ you state for January and December take account of the steady growth? Or are they the seasonal patterns you might expect to see in a steady state? In other words, do you want January figures to match the next December or the precededing December? From your comments, I will assume the latter.

What you need to do is

(a) find a smooth trend curve that fits the annual forecasts to smooth monthly foreceasts over the $48$ months;

(b) adjust these monthly forecasts by your sesonality percentages (e.g. multiply the smooth monthly forecasts by the percentages and by $12$); and

(c) adjust the results slightly so that they add up to the correct totals and are sensible across year-ends and anything else you might need such as integer values

For example, you could end up with some pattern like this

     Month 01 02 03 04 05 06 07 08 09 10 11 12
           == == == == == == == == == == == ==
 Year 1     1  2  9 11  9  5 11  6 14  7 16  9
 Year 2    10 11 36 40 29 15 32 17 35 18 38 19
 Year 3    19 20 58 58 39 19 40 20 41 21 43 22
 Year 4    23 24 70 72 49 25 52 26 52 27 53 27

noting that each January is less than $5\%$ of its year's total and each December is more than $5\%$ of its year's total, but that this is due to the trend rather than the seasonality factors