Weekly cycles and weekly activity trends do not remove inter-event burstiness for 24,231 actors in 21 activity datasets under cross-fitted Poisson rate models

Question: do daily and weekly cycles and changes in activity level explain bursty event timing of individual people? Approach: we used 21 public timestamped datasets from Netzschleuder (company e-mail, student SMS, Facebook wall, Linux kernel list, Slashdot, Digg, three Stack Exchange sites, Wikipedia user talk in 12 languages). We analysed 24,231 actors with at least 100 events. For each actor we estimated an hourly rate from data that excludes the tested week: an individual hour-of-week profile, multiplied by a weekly activity level from neighbouring weeks. We rescaled time with this rate and compared burstiness B and local variation LV with Poisson simulations that use the same rate and the same estimator. Results: the individual weekly cycle alone removed almost no burstiness (median LV 1.731 to 1.707; B unchanged at 0.598), except in company e-mail. Cycle plus weekly trend removed a median 44% of the B excess but only 1.4% of the LV excess (median B 0.358 against a null of 0.056; LV 1.714 against 1.082). All 21 datasets kept a paired excess over their own null for B and LV, with 95% bootstrap intervals above zero. 97.5% of actors had LV above their null. The result was stable across 8 changes of shrinkage, trend window, trend floor, and minimum event count. When events closer than 1 hour were merged into one, with the same merge applied to the null, the B excess stayed in all 21 datasets and the LV excess in 18. In company e-mail, SMS, and Digg votes, local clustering was only at scales below one hour. A positive control with 5-minute bursts kept LV near 1.85 after rescaling. Limitations: UTC times without daylight-saving correction; only active users; non-periodic rate changes faster than one day are not separated from bursts; actors are treated as independent in the bootstrap.

burstiness · human dynamics · inter-event times · circadian rhythm · time-rescaling theorem · local variation · temporal networks · Wikipedia · Stack Exchange · e-mail · SMS · Poisson process · activity patterns