From the training data you have displayed in the link, it is pretty clear that the choices are not exchangeable, so this is not a simple Bernoulli sequence.
Instead, it seems that your subject tends to choose a long string of consecutive values of the same type and then switch occasionally. It is reasonable to conjecture that subjects would tend to forget their previous choices once they become far away, and so it might be the case that their choice depends only on the previous choice, and how long they have been pressing it.
In This Article
This would lead me to start by trying the following conjecture and model. Conjecture 1: Subject choice depends only on the previous choice and the number of consecutive values of that choice in the present string.
We assume that subject behaviour is symmetric with respect to the choices. Conjecture 2: Subject choice depends only on the previous choice and the number of consecutive values of that choice in the present string.
We do not assume that subject behaviour is symmetric with respect to the choices. We can again specify a parametric form for these functions, model the data and estimate the functions, which then gives a basis for making predictions of future 100 predictions for binary options.
They are a financial instruments that allow you to speculate on the future market movements of the asset the option is based on.
Testing the conjectures: The above model forms would allow you to model your data under some basic conjectures about subject behaviour. Testing these conjectures could be done in a number of ways, either by nesting these models inside a broader model and doing explicit cross-validation, or by doing some kind of hypothesis test for the conjecture by formulating a test statistic that becomes large when the conjecture is false.
I will leave it to others to specify other models that could be applied to this type of data.
There are a myriad of possibilities, but the above strike me as reasonable models to start with. Have a look at the RMSE of predictions from such a model and see if they are any good.