adding skewness and kurtosis to CAPM - regression

#1
Suppose I have a set of monthly returns of a stock, monthly 'market' returns and some risk free rate for lets say 10 years. Performing an usually OLS regression to find the beta in CAPM is relative easy with the excess return of the stock as dependent variable and the excess return of the market as independent variable.
That will give me the intercept (alpha) and the coefficient (beta). In R lm(ExStock~ExMarket, data=data).

Suppose I want to add systematic skewness and systematic kurtosis (higher moments of CAPM) to an OLS model, how would I perform this regression?

The higher moments of CAPM can be found for example in this paper page 19. http://erasmus-mundus.univ-paris1.fr/fichiers_etudiants/2952_dissertation.pdf