Your friend has asked you to help them understand any potential problems that might arise in a model they have been asked to analyse. The model your friend has estimated is based on the Capital Asset Pricing Model and is:

SR_t = β₀ + β₁(RM_t − RF_t)+ β₂∆SI_t + u_t

where the daily returns for the stock are denoted by SR_t, RM_t is the market rate of return, based on an index of stocks and RF_t is the risk free rate of return. ∆SI_t is the daily change in the level of a sentiment index, SI_t, which is designed to summarise how a group of analysts feel about the stock in question. Typically SI_t goes up when the company’s stock is considered to be underpriced and goes down when it is considered overpriced.

Your friend was searching online and found mention of various potential problems relating to regressions including heteroscedasticity and autocorrelation in regressions. Your friend has sent you an email asking for your help in identifying whether this is something they should be concerned about, as they are unfamiliar with the two terms.

(a) Explain the difference between heteroskedasticity and autocorrelation in the context of the model above.

(b) Your friend claims that neither heteroscedasticity nor autocorrelation will mean the parameter estimates, when estimated by Ordinary Least Squares, are inconsistent. Your friend then claims he cannot see why they should worry about these problems, even if they exist. Discuss these claims.

(c) Explain to your friend how they can test for the presence of autocorrelation and heteroscedasticity in their model.