I would like to get some insight on what mathematical tool to use for the following problem:
I've got a time series which I'm modelling using 5 possible models. Now let us say that 55% of this time series is represented by model 1, 3% by model 2, 5% by model 3, 2% by model 4 and 35% by model 5. Now I want to get a figure which tells me that most of the data is represented by 2 models without having to set a threshold of the percentage covered by say 2 or 3 models.
What I tried to do was to order the models by the percentage of data they represent i.e
Model 1: 55%
Model 5: 35%
Model 3: 5%
Model 2: 3%
Model 4: 2%
I then gave a number to each model such that I now have:
1: 55%
2: 35%
3: 5%
4: 3%
5: 2%
Then I calculated a weighted average to give:
(55*1 + 35*2 + 5*3 + 3*4 + 2*5)/100 = 1.62
This means that on average 1.62 models represent the data well.
I am not confident that this is the right way to do it.
Any suggestions?
Thanks in advance.