Problems Arising from Autocorrelation:

Let us see what happens if we ignore autocorrelation, when it exists. The  standard software package after ming  a regression usually not only gives  the estimate β₂, but  also an estimate of its variance  (under  the standard assumption of no autocorrelation)  var (β₂)  .  Although  the estimate β₂, is  consistent,  that is  it converges to the  true value of β₂, as  sample size  increases, some serious issues  remain as  follows:  

1  )  The residual variance is likely  to underestimate  the true σ².

2)  As a result, we are likely to overestimate R²

3)  Even if σ² is  not underestimated, from equation we saw  that var  (β₂)  will underestimate var (β₂)_AR, (given the factor in parentheses there which is non zero as long as ρ ≠ 0.  It is strictly larger in most cases arising in the real wbrld since the regressors are usually positively autocorrelatcd  themselves.

4)  Therefore,  the usual  t and F  tests of significance are no longer valid, and  if applied, are likely to give seriously misleading conclusions about  the statistical significance of the estimated regression coefficients. It is more likely that we find an insignificant relationship, falsely.