Page 26 - FINAL CFA II SLIDES JUNE 2019 DAY 3

What is serial/auto correlation?
READING 8: MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS
Residual terms correlated with each other – 2 Types!
MODULE 8.7: SERIAL CORRELATION

• Positive serial correlation (SC): + regression error in one time period increases probability of a +ve regression error the next period
• Negative serial correlation (SC): + positive error in one period increases the probability a – ve error in the next period.

Effect of SC:

+ SC, due to close clustering of the scatter points, results in VERY SMALL coefficient SEs (estimated coefficients not impacted); So?
• Larger t-statistics = More Type I Errors (Rejection of Ho when it is actually true).
• Unreliable F-test due to underestimated MSE, leading again to too many Type I Errors.

Detecting Serial Correlation – 2 methods!
1) Residual plots
Error terms are + SC (r > 0). Error terms are - SC (r < 0).
Error terms are homoskedastic
and not SC (r = 0).
Use DW statistics tables for upper and lower critical DW-values (d and d ):
u
l
H : the regression has no positive serial correlation
0
Decision rule: can be inconclusive
2) Durbin-Watson (DW) statistic. We know clustering of
+ve but not
–ve so be careful!

If n very large: DW ≈ 2(1 − r) DW < d d < DW < d DW > d u
r = correlation coefficient between l l u No evidence that the error
residuals from one period and a prior period. terms are + correlated