I have a dataset of 400 time series. I want to evaluate if there is some relationship between consecutive data points. Thus, I have calculated the auto-correlation (AC) of the time series with different lags. For the best lag value, I obtain an auto-correlation of about 0.59 on average.
Now my problem is how can I know if this is a good AC value? Is there some way to evaluate if an auto-correlation value like 0.59 is good?
I have tried the following approaches to evaluate if this is a good value.
I have calculated the AC of random sequences to compare it with the AC of my time series. I have found that the AC of random sequences is always close to 0. This is interesting as 0.59 is far from 0 but still does not tell me clearly if 0.59 is a good value.
I have thus decided to do another experiment to compare the AC of my time series with the auto-corrrelation of an ascending time series (a function that is linearly increasing) and a random time series. In that experiment, I randomly tamper each sequence according to a tampering ratio that is varied from 0 to 100%. The result is like this:
It can be observed that the AC of my time series is close to that of the ascending time series and decrease quickly when the tampering ratio is increased. This seems to indicate that there is a good AC in my time series. However, it does not really tell me what is a good value for the AC.
Thus, is there other ways to determine what is a good AC value? Or do you have any other suggestions about how to determine what is a good AC value?