# How can I model this data?

The place that I work has different groups of portfolios (x1, x2, x3, ...) worth different values. Each month there are transactions with these portfolios, and their value decreases each month. The acquisitions happen in different times, so the data size for each portfolio varies.

What I want to do is construct a model to predict the way the portfolios decrease until their values become 0. Below is a simple illustration of the data:

Month,x1,x2,x3,x4,x5,x6,...,x30
1,100%,100%,100%,100%,100%,100%,...,100%
2,98.3%,98.4%,97.6%,97.9%,98.4%,no data,...,no data
3,97.6%,97.3%,96.9%,96.3%,no data, no data,...,no data
4,96%,96.5%,95.4%,no data,no data, no data, ..., no data
5,95%,95.2%, no data, no data, no data, no data,...., no data
6,94.2%, no data, ..., no data


There are three options:

• you assume that the size of the decrease is only dependent on the $month_i$ you are in

$Y = \sum \alpha_i \times month_i + \epsilon$

• you assume that the size of the decrease is only dependent on the $portfolio_i$

$Y = \sum \beta_i \times portfolio_i + \epsilon$

• you assume that the size of the decrease is dependent on the month you are in and the portfolio, but not there interaction

$Y = \sum \alpha_i \times month_i + \sum \beta_i \times portfolio_i + \epsilon$

All these options require that you reshape the data to

Month Portfolio Decrease
1 x1 -1.7%
2 x1 -0.7%
Etc.


Note that I represent it as a linear model, but it could be any kind of model.

If it suits your goals you can also add the decrease of the previous month or the absolute percentage of last month as a feature.

• Exactly, thanks! I think I'm looking for something like the third equation. Can you direct me some reference about it? Commented Oct 25, 2016 at 0:15