Question #114

Serial correlation, which is sometimes referred to as autocorrelation, occurs when the residual terms are correlated with one another, and is most frequently encountered with time series data. Positive serial correlation can lead to standard errors that are too small, which will cause computed t-statistics to be larger than they should be, which will lead to too many Type I errors (i.e. the rejection of the null hypothesis when it is actually true). Serial correlation however does not affect the consistency of the regression coefficients. (Module 1.3, LOS 1.h) Peter Pun, an enrolled candidate for the CFA Level II examination, has decided to perform a calendar test to examine whether there is any abnormal return associated with investments and disinvestments made in blue-chip stocks on particular days of the week. As a proxy for blue-chips, he has decided to use the S&P 500 Index. The analysis will involve the use of dummy variables and is based on the past 780 trading days. Here are selected findings of his study: RSS 0.0039 SSE 0.9534 SST 0.9573 R-squared 0.004 SEE 0.035 Jessica Jones, CFA, a friend of Peter, overhears that he is interested in regression analysis and warns him that whenever heteroskedasticity is present in multiple regression, it could undermine the regression results. She mentions that one easy way to spot conditional heteroskedasticity is through a scatter plot, but she adds that there is a more formal test. Unfortunately, she can't quite remember its name. Jessica believes that heteroskedasticity can be rectified using White-corrected standard errors. Her son Jonathan who has also taken part in the discussion, hears this comment and argues that White corrections would typically reduce the number of Type I errors in financial data.