Results 1 to 6 of 6

Thread: Can someone please help me interpret a cross correlation plot?

  1. #1
    Newbie
    Joined
    Oct 2017
    From
    Helsinki
    Posts
    3

    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.

    Can someone please help me interpret a cross correlation plot?-charpicea.png
    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!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,879
    Thanks
    2473

    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

    $CC(\tau) = \displaystyle \int_{-\infty}^\infty~X(t)Y(t+\tau)~dt$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2017
    From
    Helsinki
    Posts
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,879
    Thanks
    2473

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

    Quote Originally Posted by mbuchan1612 View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2017
    From
    Helsinki
    Posts
    3

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

    Hmm, in this case, how do I know how long a lag represents?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,879
    Thanks
    2473

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

    Quote Originally Posted by mbuchan1612 View Post
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Least squares and auto and cross correlation.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Jan 24th 2015, 02:17 PM
  2. Replies: 3
    Last Post: Feb 26th 2013, 11:03 PM
  3. Cross Correlation and Convolution
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 12th 2012, 06:04 PM
  4. What is the cross-correlation function of two gaussians
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 25th 2010, 03:59 AM
  5. Cross correlation
    Posted in the Math Software Forum
    Replies: 1
    Last Post: Jun 22nd 2009, 07:03 AM

Search Tags


/mathhelpforum @mathhelpforum