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 \({x}_{i}(t)\) for each business \(i\) is collected. Data processing: The ‘mid-quantiles' of each series \({x}_{i}(t)\) are computed to determine transformed individual time series \({q}_{i}(t)\) for each business \(i\). The aggregate time series \({r}_{PIT}(t)\) is transformed by a shifting and rescaling to have mean zero and variance one (\({\tilde{r}}_{N}(t)\)). The probability integral transform is then applied to form a final transformed time series \({r}_{U}(t)\) 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.