1. ## Can someone please help me interpret a cross correlation plot?

Hi everyone,

I was wondering if someone could help me by explaining in simple terms what this cross-correlation plot is showing?
The two time series I am showing are:
X = Changes in charcoal particles in sediment throughout time.
Y = Changes in spruce pollen percentage throughout time.

I am very unsure of what the lag represents so if someone could explain that, I would appreciate it very much.

I am complete beginner at cross-correlation and trying desperately to learn it quickly!

2. ## Re: Can someone please help me interpret a cross correlation plot?

Imagine your two time series as pieces of a waveform (or samples thereof).

To find a cross-correlation you lay these down on top of each other so that $t$ of the first series aligns with $t+\tau$ of the second series, multiply them and integrate them over time.

This $\tau$ is known as the lag.

putting this in math terms

$CC(\tau) = \displaystyle \int_{-\infty}^\infty~X(t)Y(t+\tau)~dt$

3. ## Re: Can someone please help me interpret a cross correlation plot?

Hi, this is great, thank you.

One last thing. If my series covers a period of 1739 years and I produce a plot with ±18 lags, how long a period does each lag represent?

4. ## Re: Can someone please help me interpret a cross correlation plot?

Originally Posted by mbuchan1612
Hi, this is great, thank you.

One last thing. If my series covers a period of 1739 years and I produce a plot with ±18 lags, how long a period does each lag represent?
The two are independent.

You can have lags as small as the time between samples.

You don't generally want to have lags approaching the duration of the time series as the correlations from such long lags are based on a very small number of samples.

5. ## Re: Can someone please help me interpret a cross correlation plot?

Hmm, in this case, how do I know how long a lag represents?

6. ## Re: Can someone please help me interpret a cross correlation plot?

Originally Posted by mbuchan1612
Hmm, in this case, how do I know how long a lag represents?
The axis of the graph is labelled and looks to be -15 to 15.. units. You're in a better position than I am to know whether those units are days or weeks or what.