Common wisdom holds it that a moving average approach is more successful than buy-and-hold. There is quantitative evidence for that across different asset classes (see e.g. this book, or this paper from the same author Mebane Faber).
My question takes a different turn: I am trying to generalize these empirical findings to a general class of stochastic processes.
What properties must a stochastic process have for moving average trading to outperform naive buy-and-hold. At the moment I am only talking about simple moving average strategies like when the process crosses the average from above/below sell/buy. There could also be simplifying assumptions like no trading costs etc.
The plan behind this is to find general properties which are empirically testable on their own. In a way I want to find the building blocks for moving average strategies to work.
Do you have some ideas, papers, references...? Thank you!