The main aim of this exercise is to learn regression techniques by applying them to the estimation of (1) in presence of (possible) anomalies in the US stock market. Each group is free to choose monthly data for a US company for the period January 2000 - September 2014. For your econometric estimations, define r_t^m and R_t^rfras the return on the relevant index and the yield on the 1-year risk-free asset, respectively.

(a) Use suitable diagrams and summary tables to discuss briefly the stylised facts relating to the returns on your chosen company and the market index.

(b) Use the OLS methodology to estimate the model described by equation (1). Briefly interpret your findings and test for misspecification in your estimated model. If misspecification is found, discuss possible remedies.

(c) Use your empirical findings in part (b) to test the restrictions: (i) α= 0 and β = 1; and (ii) β = beta of relevant sector index. Briefly interpret your findings.

(d) Use your findings in part (b) to test the stability of the estimated parameters of equation (1). Do so using a Chow-test of parameter stability, defining the tested break point to be July 2007. Repeat the analysis of part (a) for the two subsamples, January 2000 - July 2007 and August 2007 - September 2014, respectively. Briefly interpret your findings and suggest potential ways forward.

(e) Modify equation (1) in a way that allows you to test for the January effect. Briefly interpret your empirical findings.

(f) Estimate the model given by equation (2) below allowing for the effects of co-skewness and co-kurtosis. Briefly interpret your findings.

R_t = α + β₁R_t^m + β₂sk_t + β₃kur_t

(g) Provide an overall assessment of your findings in parts (b) to (f) regarding the most suitable model to explain the returns of your chosen company. Make suggestions for any possible ways to improve the model.