the cone of influence at that scale. Assuming a background spectrum given by Eqn. \[fouriereqn\] we estimate the autocorrelation coefficient ($\alpha$) by calculating the lag-1 and lag-2 autocorrelations, $\alpha_{1}$ and $\alpha_{2}$. The autocorrelation coefficient is then estimated as $\alpha = (\alpha_{1} + \sqrt{\alpha_{2}})/2$. The background spectrum $P_{j}$ then allows us to compute the confidence levels. It is assumed that the time series has a mean power spectrum given by Eqn. \[fouriereqn\] and so if a peak in the wavelet power spectrum is significantly above this background spectrum, then the peak can be assumed to be a true feature. If the values in the time series $f(t)$ are normally distributed, we expect the wavelet power $|\widetilde f|^{2}$ to be $\chi^{2}$ distributed with two degrees of freedom ($\chi^{2}_{2}$). The square of a normally distributed variable is $\chi^{2}$ distributed with one degree of freedom and the second degree of freedom comes from the fact that both the real and imaginary parts of the complex $\widetilde f$ are normally distributed. For example, to determine the 95$\%$ confidence level, one multiplies the background spectrum (Eqn. \[fouriereqn\]) by the 95th percentile value for $\chi_{2}^{2}$. In Figure \[sinegwps\] we show the GWPS of a time series along 