Correlating with a random time series

To correlate, simply choose "Random" from the Time Series options. A different random time-series will be generated for each plot created.
Significance Determination of Correlation Values
Determining whether the map you get back from performing a correlation of an atmospheric variable with an index time-series shows a real physical relationship is a difficult problem. I provide a discussion of the mathematics which should help. However, because of the high spatial correlations that exist in most atmospheric fields and because of the positive autocorrelation in many index time-series, it is easy to see patterns that just happen by chance. This can be illustrated by using the random time-series and examining the patterns that result. Try running the correlation a few times to see how these spurious correlations can look "real" in at least some cases.
Random Time-series: Calculation details
The time-series you get is a randomly calculated "red noise" time-series. In this case, the solution is calculated from the integrated stochastic differential equation

           dx/dt = (-1/T)x + whitenoise.

1/T is set to -1/3 months or -.333 for all cases. x(t=0) is determined using a changing seed value and the white noise is obtained by sampling from a gaussian distribution. Values are set for all 12 months of 1958-1999 and seasonal values are calculated from that. Code was graciously provided by Cecile Penland of CDC. Other definitions of a random time-series could have been used.

Please do not try to do Monte Carlo tests by repeatedly running the web-page.

Back to main correlation page.
Background Information
Related Plot/Analysis

In order to help ensure that this web analysis page remains available, we would greatly appreciate feedback on its use, particularly in the classroom, for presentations or for research. Mail feedback to PSL data