# Why is the correlation between two data series negative when the top half and bottom half are both strongly correlated?

I have two time series of data variables with each having 111 data points.

The data series should be strongly correlated given the nature of what is being explored.

However, the correlation between the data series is roughly -0.03 which confused me.

To explore further, I checked the correlation between data points 1-62 and 63-111 separately.

The correlation between the data series for points 1-62 was 0.83 and the correlation between the data series for points 63-111 was 0.55.

It is surprising to me that it is -0.03 for the whole series when they're positively correlated when split into two subsections.

Is this possible or am I making a mistake?

• This sounds like a version of simpson's paradox. Is there a substantial change between 62 and 63? Have you tried plotting the data? – David Luke Thiessen Feb 27 at 14:55

Here's an example of a dataset which does not exhibit any correlation between the variables C-1 and C-2, though the individual parts (the first half and the second half of the data points) are highly correlated: 