Hello

Since Logit and Probit merges mostly for binary or binomial, the auto correlation will be of higher significance. However below binary and above binary the significance could vary on many other parameters.

Regards

Hello,

Thank you very much for answering, but I do not know how to perform a formal test. Any suggestion of references would be appreciated.

You can try to use the runs test.

https://en.wikipedia.org/wiki/Wald%E2%80%93Wolfowitz_runs_test

Thank you very much. Could you explain more about how to do the run test? I do not get how to use the output from logistic regression which is the estimate of the probability, to do the run test.

Suppose y[t] is our time series, y^[t] is the output from your model. You first need to construct the residuals series, r[t].

Do the following:

for each t: if y^[t]>=0.5, p[t]=1, else p[t]=0 (p[t] is just some aux. variable).

for each t: r[t] =y[t]-p[t]

After you have r[t], use the runs test by following the instructions in the above link. Replace 0 with + and 1 with - (or vice versa, it does not matter).

P.S. Theoretically,  + and - must be randomly distributed if you have no auto-correlation..

Thank you very much. Now it has become clear how to implement it. Do you know of any article or text book, so that I mention it in my reference for this ? 

You're welcome. I'm not aware of any at the moment.