tfest() function using - set initial condition for output value

Good day

Could you help me please to figure out if i have an opportunity to set initial conditions of output signal for estimated transfer function?

I'm trying to estimate a TF based on data above: input signal is orange one, output signal is blue one. The yellow one is what i get, if i set the input signul to estimated TF.

If i substract from my real output value the initial point (the value is 511), the the estimation goes well and i got good result. But as i understand it would be the wrong TF

I know that we can set the initial value of input signal, but do we have an oppotrunity to do it for output?