How do correlations behave in real world?

[Stuti]

• Time lag 2 autocorrelation is highest, so autocorrelation with respect to two months prior produces the highest autocorrelation. Altogether we observe the expected decay in autocorrelation with respect to time lags of earlier periods.
  

This result shows that current prices will be less dependent on the stock prices further back in time and hence will have a lower autocorrelation than with with the prices in the near past and will have a higher autocorrelation?