I'm studying several time series. The variables of interests are dummy variables which take value 1 when a certain event happened, 0 otherwise. I want to find the best distribution to describe these data. I'm using the function
fitdistr() of R, which allows me to use as discrete distributions the Poisson and the negative binomial. I've found using a chi-square test that the Poisson describe really well these data (p-values all over 0.90, so I do not reject the hypothesis that the data are distributed following a Poisson).
My question is: can a Poisson distribution be considered a good model to describe binary data? The hypothesis testing suggests that it is, I want to know if there are theoretical drawbacks or statistical errors in such fitting. Thank you.