Intermediate CLV results need to be stored

[haseeb1431]

          > Can we get the intermediate results output as well such as prediction at each month level so that we can reuse the data and avoid running predictions again and again. [I think it's not possible as per the code](https://github.com/pymc-labs/pymc-marketing/blob/aef97917e72f26f247cd6be83274f52895cdad4f/pymc_marketing/clv/utils.py#L134C2-L148C10) unless we update it to store the monthly values. Thoughts?

CLV is calculated progressively. Let's say if we want to calculate the CLV for 1, 3, 5, 7, and 10 years. Now I call the expected_customer_lifetime_value for each year (1,3,5,7,10 separately) and it starts calculating from month 0 every time. As we know CLV calculation is progressive so If I calculate the CLV for 10 years, internally we have calculated the CLV for all the years from the first year till year 10.

• Year 1 CLV will calculate all the months from 1 to 12
• Year 3 CLLV will calculate all the months from 1 to 36 (including the 12 months which we calculated last time)
• Year 5 CLLV will calculate all the months from 1 to 60 (including the 36 months which we calculated last time)
• Year 7 CLLV will calculate all the months from 1 to 84 (including the 60 months which we calculated last time)
• Year 10 CLV will calculate all the months from 1 to 120 (including the 84 months which we calculated last time)

So there are a lot of calculations that are repeated. What I wanted is that if we calculate the CLV for 10th year, Can we get the intermediate results output as well such as prediction at each month level so that we can reuse the data and avoid running predictions again and again. I think it's not possible as per the code unless we update it to store the monthly values.

[ColtAllen]

It's possible for purchase probabilities to be estimated across various time intervals:

• Add Time Interval Selection for BetaGeoModel Expected Purchases #218
• Additional enhancements for ParetoNBDModel #183

However, this is not the case for expected purchases. Computationally there is no difference; just need to write the results for every iteration.