7. AUTOCORRELATION TEST
• The test requires the computation of
autocorrelation between every m numbers,
starting with the ith number .
• Thus the autocorrelation ρim between the
following numbers would be of interest:
Ri , Ri+m, Ri+2m, .. .. .. .., Ri+(M+1)m.
8. AUTOCORRELATION TEST
• Where M is the largest integer such that
i+(M+1)m<=N , where N is total number of
values in sequence.
• A nonzero autocorrelation implies a lack
of independence, so following two tailed test
is appropriate: H0 : ρim = 0
H1 : ρim ×= 0
9. AUTOCORRELATION TEST
• For large values of M, the distribution of
the estimator of ρim , denoted ρim is
̂
approximately normal if the values Ri , Ri+m,
Ri+2m, .. .. .. .., Ri+(M+1)m are uncorrelated, then
the statistics can be as follows:
Z0 = ρ̂ im
σρ
im