I've got these two acf plots that were produced in R. The first plot is the acf of a differenced time series (in this case tweets from twitter). The second plot is the acf of the remainder component of the decomposition of the same time series (in other words the leftover random noise). The problem I have is establishing which of these series shows a higher correlation.
The acf of the remainder component suggests that it is close to random noise (which would be expected as the trend and seasonality components have already been extracted). Most of the lags though are above the confidence interval suggesting that there is some (small) statistical significance to the correlation.
The differenced time series shows a moderate negative correlation for the first lag and then no significant correlation thereafter.
My question then is does the remainder acf show more correlation because more lags are above the confidence interval (even though they are small) or does the differenced time series show more correlation because it has a single strong-ish correlation?