Figure 5

Intricate dynamics of sociotechnical time series. Panels (A) and (D) show the time series of the ranks down from top of the word “bling” on Twitter. Until mid-summer 2015, the time series presents as random fluctuation about a steady, relatively-constant level. However, the series then displays a large fluctuation, increases rapidly, and then decays slowly after a sharp peak. The underlying mechanism for these dynamics was the release of a popular song titled “Hotline Bling”. To demonstrate the qualitative difference of the “bling” time series from draws from a null random walk model, the details of which are given in Appendix 1. Panels (A), (B), and (C) show the discrete shocklet transform of the original series for “bling” and the random walks \(\sum_{t'\leq t} \Delta r_{\sigma _{i} t}\), showing the responsiveness of the DST to nonstationary local dynamics and its insensitivity to dynamic range. Panels (D), (E), and (F), on the other hand, display the discrete wavelet transform of the original series and of the random walks, demonstrating the DWT’s comparatively less-sensitive nature to local shock-like dynamics