How to explain the difference between the following time series?

Question

I am conducting an empirical study for understanding the behavior of different people in a collaborative environment.

There are two types of events in my study: A and B.

Let's assume A means focusing on the work and B means talking to another person.

There are generally two kind of patterns that I observe:

1. A A A A B B A A A A B B A A A A B B A A ... (Focusing a little bit and discussing a little bit)

2. A A A A A A B A A A A A A A B A A ... (Focusing for a relatively long period of time and discussing for a short period of time)

How can I statistically explain the difference between these two time series of events?

Answer 1

Sorry I don't have the reputation to just comment.

It looks like you want a rigorous way to write down two sequences.

Try converting A's to 0's and B's to 1's. Then the top sequence is a rational number and the second looks like it will be transcendental, but it's hard to tell without seeing more terms.

Answer 2

The system won't let me comment because of my reputation.

Assuming the run length follows a Poisson distribution, you can get the average run length and conduct test on that