So we started with as simple a model as possible,

saying let's just assume it's a coin flip.

Each time period, there's a constant probability of churn

that was our geometric model.

And we saw okay, it's not great,

we saw that's essentially splitting the difference.

But when we look at the overall forecast,

we see that the geometric model just doesn't do that well for us.

Yes, it captures the overall shape, but

sometimes it systematically over-predicting or

under-predicting churns in other time periods goes the other way,

whereas allowing for the model with time varying churn rate,

we'd going to end up with a very much better forecast.

Now, one of the things we'll talk about a little bit later in the course, something

that's kind of pushing the limits of Excel is what's driving this dynamic.

Two potential explanations.

One is that individuals are literally changing over time becoming more and

more loyal, less and less likely to churn.

The other explanation is that the individuals who remain

later on are fundamentally different than the individuals who remain early on.

So, one explanation is dynamics in the churn probability.

The other explanation is heterogeneity across the user base.

Ideal model is going to combine both of those factors.

So we'll talk a little about unobserved heterogeneity,

the importance of heterogeneity later in the course, but again,

it's something that is really pushing the limit of what Excel can do,

better suited to a computing environment, such as R and MATLAB.

But in terms of, yeah, accuracy of the model, just bringing in a simple time

trend here, a linear time trend, does much better than ignoring that time trend.

And so we are able to pick up some of the dynamics that occur in that churn rate.