Force predictions of 2 time series models with different time steps to be consistent

Question

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?

Answer 1

1. It depends on the models you have trained.
2. What you are looking for is a harmonized predictions from different models that is really hard to obtain.
3. Even this was not your question, but I want to ask you why you need two models to predict the sales?

My solution (to get weekly and monthly sales forecast):

Build 1 model for weekly sales forecast. Derive Monthly sales by using pandas Groupby functions.

monthly_sales_foreast = weekly_sales_forecast.groupby(pd.Grouper(freq='1M')).sum()

or by number of days

monthly_sales_foreast = weekly_sales_forecast.groupby(pd.Grouper(freq='30D')).sum()

In case you are using the same inputs, you can e.g. build a model first for the weekly prediction and change the output layer dimension of model afterwards to obtain monthly forecasts from the same model.

Check out articles about Transfer Learning. I think you will find examples with a global base model and updated different models and additional inputs.

I hope this helos you to get closer to your required solution.