There are various studies concerned with the estimation of stochastically varying coefficients for the hedge fund series but just [sic] few are available in the literature that study the model with time-varying coefficients and non-linear factor, or make a comparison of the series before and during the financial crisis. This work studies a model with linear and non-linear factors with stochastically varying coefficients to obtain better estimation of the exposure of the hedge fund and accuracy in the results. Better exposure estimates implies better hedging against negative changes in the market hence a reduction in the risk taken by the hedge fund manager. Besides, different techniques have been studied, implemented and applied in this thesis to estimate and analyze time varying exposures of different HFRX Index (an index that describes the hedge fund industry performance).The study shows that option-like models with time-varying coefficients perform the best for most of the HFRX indexes analyzed. It also shows that the Kalman Filter technique combined with the Maximum Likelihood Estimator is the best approach to estimate time-varying coefficients. In addition, we provide evidence that Kalman Filter is in a better position to capture changes in the exposure to the market conditions.