and here we follow @tor98. First, one compares the wavelet power with that of an appropriate background spectrum.

We use the univariate lag-1 auto-regressive \[AR(1)\] process given by $$\label{noiseeqn}
x_{n}=\alpha x_{n-1} + z_{n}$$ where $\alpha$ is the assumed lag-1 autocorrelation and $z_{n}$ is a random deviate taken from white noise. Note that $\alpha = 0$ gives a white noise process. Throughout this paper, we will use “white noise” to refer to an AR(1) process with $\alpha = 0$. Red noise is sometimes used to refer to noise with $\alpha = 1$, however, throughout this paper we apply the term to any non-zero $\alpha$.

The normalized discrete Fourier power spectrum of this process is $$\label{fouriereqn}
P_{j}=\frac{1-\alpha^{2}}{1 + \alpha^{2} - 2 \alpha \cos(2 \pi \delta t /\tau_{j})}$$ where $\tau_{j}$ is the associated Fourier period for a scale $l_{j}$. We use the above two equations to model a white noise or red noise spectrum.

The global wavelet power spectrum (GWPS) is obtained by averaging in time $$\widetilde f_{G}^{2}(l_{j})=\frac{1}{N_{j}} \Sigma^{i'_{j}}_{i=i_{j}}|\widetilde f(l_{j},t'_{j})|^{2}.$$ Here, $i_{j}$ and $i'_{j}$ are the indices of the initial and final translations $t'_{i}$ outside of the cone of influence at a given scale $l_{j}$. $N_{j}$ is the number of translations $t'_{i}$ outside 