For example I know that we sold 5000 pieces of something in previous month. I know that month split into weeks and every month we sell on 20% more than in previous month. This is some kind of global trend that goes for years.
So I can know exact amount of sales every week by using this scheme: Month split into 4 weeks and we sold 5000 things in that month. First week we selling 100%, second is 105, third is 110 and last one is 115.
We can use this as coefficients:
1 week 2 week 3 week 4 week /*Total 5000 things*/
100 105 110 115 /*we can summ coeffs and get 430*/
0.2325 0.2441 0.2558 0.2674 /*we divide 100/430, 105/430 and etc to normalize it*/
1162.5 1220.5 1279 1337 /*we multiply 0.2325 on 5000 to get sales amount in first week and etc*/
And that's really working, each of these values 1162.5, 1220.5, 1279, 1337 greater than previous on 5%.
But that's where things gets unclear. We also know that there is seasonal changes. We know that fist week we sell a little bit less, than in second, in second a little more, then third, and third is way bigger, than last. We can describe that seasonal changes as another set of coefficients:
1 week 2 week 3 week 4 week /*Total 5000 things*/
0.9 1 0.9 0.5 /*summ is 3.3*/
0.2727 0.3030 0.2727 0.1515 /*normalized*/
1363.5 1515 1363.5 757.5 /*real sales per week*/
So we calculated separately each week sales like if we had global trend only and seasonal changes only, but how we can mix those?
I don't know what to do with 1337 and 757.5 for last week and etc.
If your second table is really direct week/week ratio and it is the same in different months as it looks from your second example, then I don't understand where your trouble is. What's wrong with simple
amount(month_index, week_index) = 5000 * ((1.2) ^ month_index) * normalized_week_coefffcient[week_index]
In other words first use your 20% per month to calculate total amount in the month and then split that total amount between weeks according to normalized week coefficients from your Table #2