System Identification - Modelling data, low fit

Hi, I am trying to estimate a process modell by a set of input and output data, but iam uncertain about the abilities and limitations of the methods i am trying. I have started by both normalizing and detrending my dataset, as shown in the figure below. The input data is an "on/off" parameter that have been choosen to be either -0.3 or 0.3 (but can be changed if it is advised).

My original thought was to attempt to modell the process by either ARX or ARMAX estimation. I tried to start with an ARX estimation where the AIC said na=10, nb=10, nk=1, with a 26.17% fit as shown below

This was clearly a higher polynomial order and worse fit than i originally had hoped. The ARMAX estimated resulted in much of the same result.

I would like to ask for some advise for my further work. Is there some more suitable method to solve the modell estimation, or will it be a hard nut to crack? I have attached the system identification toolbox file for the dataset.