### Correlating with a random time series

*Directions*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 equationBack to main correlation page.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.