In this book, we present several new empirical models and new estimation methods for financial models of returns. Our new empirical models are based on a generalized version of the Hausman test using higher moments and cumulants. Our methods rely on higher moments and cumulants as instruments to improve the well-known GMM technique, which we call the GMM-C or the Haus-C estimators. Then, we generalize these new estimators to panel data resorting to our new empirical models of hedge fund returns. Finally, we feature an innovative application of the Kalman filter for our new empirical models of hedge fund returns, in order to obtain a dynamic version of the alpha and beta parameters.