Autocorrelation and evidence of iid Suppose I have the first seven autocorrelations for some variable $x$.
And suppose they are -0.2, 0.15, -0.05, -0.10, -0.05, -0.14, 0.04
How can this be used as evidence of my data being or not being IID (suppose $n=150)$.
 A: Are you working in R? Plot the ACF function with the confidence intervals, if one of your autocorrelation values [-0.2, 0.15, -0.05, -0.10, -0.05, -0.14, 0.04] for the first seven lags exceeds this confidence interval, you know it is significant.
http://stat.ethz.ch/R-manual/R-patched/library/stats/html/plot.acf.html
You can also calculate it manually. The 96% confidence interval of the autocorrelation is given by [ $-1.96/ \sqrt{n}$ to $1.96/ \sqrt{n}$ ], which is in your case with n=150 [-0.16 to 0.16]. So given the autocorrelation of your first seven lags, we would conclude that there is significant correlation of an observation at time T with an observation at T-1.
A: Have you only the first seven autocorrelations or are you able to compute everything you want? Have you all the values of x? 
If that is the case, I guess you could try the Durbin-Watson test. It is used to detect non-null autocorrelation. There may be more information in this pdf.
A: In addition to others' comments, I would advocate plotting the variogram for these data which is very effective at showing temporal or spatial sources of correlation in data. You can estimate the kernel and nuggets of such plots to determine the strength of correlation and the amount of dispersion in these data.
