# How to estimate the deposit mix of a bank using interest rate as the independent variable?

Let's say a bank has 5 different types of deposits. One type is certificates of deposits (CD), and the other 4 types are different checking and savings account products with various interest rates levels.

The deposit mix represents the sum of the % of deposits allocated to each of the 5 product types. That sum obviously equals 100%.

I want to figure how that deposit mix shifts in response to interest rate levels (proxy is probably the US Federal Funds rate). The hypothesis is that as interest rate level increases the deposit mix will shift more and more towards CDs and away from the other products and vice verse. It makes sense, but is it true?

I probably will work with a good time series of monthly observations in deposit mix for over 8 years or so.

I was thinking maybe this is a Discriminant Analysis (DA) problem. But, I fear DA may not handle % variables that are not categorical variables with binomial outcomes (1, 0). I was also thinking maybe this is a Logit Regression (LR) problem. But, there is also the issue of the variables not being categorical. And, can Logit handle more than one dependent variable? In this care there are essentially 5.

So, how would you handle this problem? Using what method? And what software? Could you do it long hand in Excel?