Suppose I have a time series. Let's say it is of the number of sales in a shop. Suppose I am looking to make two models - model 1 which predicts future values by weekly time steps (total sales per week, i.e. 1-7 days from now, then 8-14 days from now, then 15-21, etc.) and model 2 which predicts future values by monthly time steps (total sales per month).
Note that I have not decided what models each of these will be yet. But I cannot assume that the data/features used to train each model will be the same.
Let's say I make predictions with both models for the period of time ranging from the start of September to the end of October (inclusive). So this is 3 months, in total consisting of exactly 13 weeks. Therefore I will have 13 predictions from model 1, and 3 predictions from model 2.
Let $S_1$ be the sum of the 13 predictions for model 1, and $S_2$ be the sum of the 3 predictions for model 2. How can I ensure that $S_1$ and $S_2$ are the same?