Modeling continuous time series with many zeros and an application to earthquakes

A leading model in earthquake forecasting is the epidemic-type aftershock sequence model, which takes the times and locations of future aftershocks to depend on previous earthquakes, with more recent earthquakes exerting more influence than older events. Such models generally involve a time-series of binary events in continuous time. In a recent paper, LML Fellow Jiangcang Zhuang and colleagues propose a discretised version of this model, with time divided into intervals of equal duration – one hour or one day, for example. The time series reflects the total energy released by earthquakes in each interval. As the authors note, such a time series will naturally have many zeros, corresponding to intervals with no earthquake activity being recorded, either because no earthquake occurred or instruments were not sensitive enough to detect activity.

Zhuang and colleagues develop an efficient forecasting method for models of this type and then test it in a retrospective forecasting experiment for seismic activity in the Canterbury region of New Zealand for the two month period following the 2010 Darfield earthquake. This earthquake lacked any significant foreshock activity, and its aftershock activity decayed with time for about 6 months until the large Christchurch earthquake on 21 February, 2011. The authors find that the forecasted daily average energy indexes were close to the observed values, reflecting high forecasting accuracy. Zhuang and colleagues hope the work will contribute a general tool for improved analysis of time series data.

The paper is available at

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