I am not enamored of using rolling 3 year returns to assess persistence.
A 3-year time period will often be all up or all down. If a fund manager has an investing personality or philosophy then I would expect strong relative performance in a rising market to be negatively correlated with poor relative performance in a falling market, etc.
It seems to me that the best way to measure persistence is over 1 (or better yet more) market cycles.
So, the question becomes:
Did those funds which outperformed in their style group (preferably on a risk-adjusted basis) continue to do so in the next complete market cycle?
One may formulate this more precisely in one of several ways, such as:
Does alpha over a complete market cycle correlate with alpha over the next cycle?
Does percentile rank within a style group over a market cycle correlate with percentile rank within the group over the next cycle? (Might get a different answer for less efficient market segments, such as small value, etc.)
What proportion of funds in a style group with the top (10%, or 25%) Sharpe ratio over a complete market cycle maintain that position?
I'd love to see more on this if anyone knows of such work.
There was a paper out of the U Mass Amherst research center on securities which looked at the alpha question, and the answer was supportive of persistence. I did a study a few years ago looking at no-load large cap value funds which had existed for at least 8 years and asked if the ranks in style group for the first 7 years could predict the rank in style group for the 8th year. The correlation between the first 7 years' rank (7 predictors) and the 8th was approximately .50, suggesting that there is some persistence.