"What happens when you change manager?
So in the Premier League, at least, there is a boost for a short honeymoon period and then performance dips back – and indeed slightly below the level that it was before the club changed manager. Between 12 and 18 games after appointment, the points’ benefit of changing manager has vanished, suggesting that on average there is only a short-term gain and a longer-term negative effect of changing manager."
From: http://www.wbs.ac.uk/downloads/news/2009/10/what-is-the-impact-of-changing-football-manag.pdf
I can't manage to insert the graphic this refers to, but essentially, there is usually a small uplift in the first 6 games after a change, with a bigger impact games 7-12, before reverting to the mean (ie where you were before the sacking). Our 'bounce' has been negligible - whether this is because of the desperate plunge we were on prior to the change or the lack of impact Remi has had is a matter of opinion.