Figure 3

A comparison between the standard discrete wavelet transform (DWT) and our discrete shocklet transform (DST) of a sociotechnical time series. Panel (B) displays the daily time series of the rank \(r_{t}\) of the word “trump” on Twitter. As a comparison with the DST, we computed the DWT of \(r_{t}\) using the Ricker wavelet and display it in panel (A). Panel (C) shows the DST of the time series using a symmetric power shock, \(\mathcal{K}^{(S)}(\tau |W,\theta ) \sim \mathrm{rect}(\tau ) \tau ^{\theta }\), with exponent \(\theta = 3\). We chose to compare the DST with the DWT because the DWT is similar in mathematical construction (see Appendix 1 for a more extensive discussion of this assertion), but differs in the choice of convolution kernel (a wavelet, in the case of the DWT, and a piece of a shock, in the case of the DST) and the method by which the transform accounts for signal at multiple timescales