Hypothesis Testing Fusion for Nonlinearity Detection in Hedge Fund Price Returns

In this paper, we present the results of nonlinearity detection in Hedge Fund price returns. The main challenge is induced by the small length of the time series, since the return of this kind of asset is updated once a month. As usual, the nonlinearity of the return time series is a key point to accurately assess the risk of an asset, since the normality assumption is barely encountered in financial data. The basic idea to overcome the hypothesis testing lack of robustness on small time series is to merge several hypothesis tests to improve the final decision (i.e., the return time series is linear or not). Several aspects on the index/decision fusion, such as the fusion topology, as well as the shared information by several hypothesis tests, have to be carefully investigated to design a robust decision process. This designed decision rule is applied to two databases of Hedge Fund price return (TASS and SP). In particular, the linearity assumption is generally accepted for the factorial model. However, funds having detected nonlinearity in their returns are generally correlated with exchange rates. Since exchange rates nonlinearly evolve, the nonlinearity is explained by this risk factor and not by a nonlinear dependence on the risk factors.