A note on statistical models for individual hedge fund returns

In recent years, a large number of research papers and monographs on the analysis of hedge fund returns have been published. Typically, the authors of these studies implicitly or explicitly treat monthly returns of hedge funds as independent and identically distributed observations. The Hedge Fund Index might be able to serve that role. But the returns of an individual hedge fund are not like that. They behave autoregressively depending on the time periods. This stochastic behavior should be modeled as a combined/regime switching stochastic process of two processes: i.i.d. process and autoregressive process. This paper first depicts the autoregressiveness of hedge fund returns. Then we introduce our statistical model for returns of an individual hedge fund and then, with our retrospective view, we perform several data analyses for individual hedge funds’ return data.