we discuss structure functions in Section \[sfpileupsection\].

Data Analysis and Results
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Wavelet Analysis {#waveletanalysis}
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### The Continuous Wavelet Transform

The continuous wavelet transform (CWT) is the inner product of a dilated and translated mother wavelet and a time series $f(t)$, the idea being that the wavelet is applied as a band-pass filter to the time-series. The continuous wavelet transform maps the power of a particular frequency (i.e. dilation) at different times in translation-dilation space, giving an expansion of the signal in both time and frequency. Hence, the continuous wavelet transform not only tells us which frequencies exist in the signal, but also when they exist, allowing us to see whether a timescale varies in time. This is the wavelet technique’s advantage over Fourier transforms in detecting quasi-periods. In addition, the Fourier transform is not suited for detecting quasi-periods since non-periodic outbursts will spread power across the spectrum and windowing will cause power to appear at low frequencies, potentially obscuring quasi-periodic signals.

Throughout this paper, we follow @hug98 and @kel03 and references within. In previous studies [@hug98; @kel03; @liu05; @kadler06] we have found the Morlet wavelet $$\psi_{Morlet} = \pi^{-1/4} e^{ik_{\psi}t} e^{-|t^{2}|/2},$$ with $k_{\psi}=6$ to be an excellent choice. The 