# ARMA: modelling a time series with a bimodal distribution

I have a de-trended and de-seasonalized time series, and it's distribution is not gaussian (see distribution in Figure 1).

I tried modelling it with and ARMA model, but as we could expect, this model does not have good prediction capabilities (see Figure 2), especially for high values / maxima.

My question is: is there a way to use auto-regresive models to model signals with bimodal distributions? If so, how can I do it in Python / R?

Figure 1:

Figure 2:

You probably used the stock arima function to model ARMA process. The stock function uses MLE with normal distribution. If you think your errors are bimodal and the process is still ARMA, then the only solution is to get into nonnormal modeling. You may need to implement your own MLE with your own error distribution.