Suppose I have a vector say:
[5 5 5 5 4 5]
then common sense says that there is a very high auto-correlation for the vector because it is more or less the same values.
But when I try to calculate the auto-correlation coefficient, I'm getting a very low value(<0.3) for all lags. What does this mean? shouldn't it be higher because the series is very similar?
Am I missing something?
does correlatiom mean not similarity but similarity in rate(Rate of change)?
A similar situation arises when you fit a regression line to perfectly horizontal data — you get a “linear” relationship that is nearly perfect but also completely uninformative.
Correlation measures how changes in X about its mean are related to changes in Y about its mean. In the case where one of the variables is (or is almost) constant, then there isn’t much variation left to attribute to the other variable: