Fig. 2. Schematic for the proposed framework to detect downtime of small businesses after natural hazard events.

Data collection: The time series of posting activity $x_i\left(t\right)$ for each business $i$ is collected. Data processing: The ‘mid-quantiles' of each series $x_i\left(t\right)$ are computed to determine transformed individual time series $q_i\left(t\right)$ for each business $i$. The aggregate time series $r_{PIT}\left(t\right)$ is transformed by a shifting and rescaling to have mean zero and variance one (${\tilde{r}}_N\left(t\right)$). The probability integral transform is then applied to form a final transformed time series $r_U\left(t\right)$ for the level of activity in the region. Downtime detection: Threshold $T^{*}$ is found using the elbow method to identify anomalous events. For a given event, the downtime length, $d^{*}$ is determined.