How do I smooth-over transition from a time-series generated by one system to a time-series generated by another system?

Question

So I have generated a time-series with length on 2N samples, where the first N are generated by one auto-regressive system and the N+1 to 2N are generated by another, similar, auto-regressive system.

Here's a picture of the transition itself:
So, around time-point 250, I have few of those small blue peaks, but what I want is a more-or-less smooth transition, as marked in red.

Any ideas on how I could achieve that, without damaging the rest of the signal?