Serial Correlation

Summaries

Serial Correlation (Autocorrelation) – usually time series

-          Positive – positive regression error increases the possibility of +ve error in the next period

o        Increase type I error (variance too small)

-          Negative - +ve regression error increases the possibility of –ve error in the next period

o        Increase type II error (variance too large)

Durbin-Watson (DW) Statistic

DW = Sum(error_i – error_i-1)^2 / Sum(error_i)^2

=2(1-r) when n is large, where r is the correlation of residual from one period to previous period

homoskedastic, DW =2

+ve serial correlation DW<2

-ve serial correlation DW>2

DW< d_l => positively correlated

d_l<DW<d_u => inconclusive

d_u<DW<4-d_u => cannot reject

4-d_u<DW<4-d_l => inconclusive

4-d_l < DW<4 negatively correlated

Use Hansen Method to adjust standard error (can help heteroskedasticity also. But if heteroskedasticity only, use White-method)