# Can I use ARIMA to model non-Gaussian time series?

I have monthly data on the number of people who have a disease, say, cold, within the study population, and I have the number of people that took certain medication when they had the cold. And I have an intervention time point to estimate the intervention effect.

To me it looks like I have a binomial distributed series. If I remember correctly a stationary series doesn't need to be normal, but I am not sure if I should fit a ARMA model on a series of proportions - the first problem I can think of is, the forecast might not be bounded between 0 and 1.

Please let me know if Box-Jenkins models are the right way to go here or should I use a glm type of thing allowing high order of correlations?

• What do you exactly want to model and why is this binomial distributed? E.g. the number of people who have a disease is not binomial distributed? You mean taking or not taking the medication and you want to model that? Please specify. And I am not getting your point of non-Gaussian time series? I mean of course there are a lot of cases where you have one realization of the true data generating process and you model that with an ARIMA model, but the distribution itself is not a Gaussian. – Jen Bohold Aug 16 '13 at 17:14
• For example consider the GDP: You have one realization (one time series) from the true data generatin process. The GDP values do not need to be from a normal distribution, but you still can try to model it by e.g. an AR(1) if the series seems to be stationary and there is a significant autorcorrelation at lag order one. I think you are not really clear about time series and especially ARIMA models or? – Jen Bohold Aug 16 '13 at 17:18
• What the researcher cares about is the proportion of people who choose to take the medication among those people who have the disease. So it is always bounded between 0 and 1. – McFluffin Aug 16 '13 at 17:35
• But then he has the proportion values over time right? So it then depends on the series if it is stationary and then it could be modeled by ARMA (otherwise check for unit root to model it with ARIMA). But it's right, that possibly forecasts result which are out of the range (between 0 and 1). Ok, now I got the problem – Jen Bohold Aug 16 '13 at 17:38
• Yes of course this is recorded over a period of a few years so I have say 50 of these proportions. My confusion is, I remember from when I took TS course the teacher said the distribution of Xt in a stationary process doesn't need to be Normal, as long as there are finite types of distribution generating the series it could be stationary. So I guess my question is if ARMA model deal with any stationary process? I've seen some discussion on that topic before but can't find the exact reference - and more practically how do I deal with the forecast issue. – McFluffin Aug 16 '13 at 17:48