phase.partnered function

Phase partnered time series

Create two time series with specific autocorrelation $\gamma$, cross-correlation $\rho$, mean ts.mean, and standard deviation ts.sd using the phase partnered algorithm described by Vasseur (2007)

phase.partnered (n = 2000, rho = 1, gamma = 1, sigma = 0.1, mu = 0)

Arguments

• n: number of time steps in time series. Default is 2000.
• rho: cross-correlation between the two time series ($-1\le \rho \le 1$). Default is 1.
• gamma: autocorrelation of each time series. Gamma ($\gamma$) describes the relationship between frequency $f$ and power $P$: $P(f)=1/f^\gamma$. If $-2\le \gamma \le 0$: blue noise and $0\le \gamma \le 2$: red noise. Default is 1.
• sigma: standard deviation of both time series. Default is 0.1.
• mu: mean of both time series. Default is 0.

Returns

Returns a named list containing the following:

• rho: Cross-correlation of the time series

• gamma: Autocorrelation of the time series

• sigma: Standard deviation of the time series

• mu: Mean of the time series

• timeseries: n x 2 matrix containing the time series

References

Gouhier, T. C., F. Guichard, and A. Gonzalez. 2010. Synchrony and stability of food webs in metacommunities. The American Naturalist 175:E16-E34.

Vasseur, D. A. 2007. Environmental colour intensifies the Moran effect when population dynamics are spatially heterogeneous. Oikos 116:1726-1736.

Author(s)

Tarik C. Gouhier (tarik.gouhier@gmail.com)

Examples

# Positively cross-correlated white noise
pos.corr=phase.partnered(n = 100, rho = 0.7, gamma = 0)
# Negatively cross-correlated white noise
neg.corr=phase.partnered(n = 100, rho = -1, gamma = 0)
par(mfrow=c(2,1))
matplot (pos.corr$timeseries, t="l", lty=1)
matplot (neg.corr$timeseries, t="l", lty=1)