Time series analyses are carried out on earthquake data from the main seismic region of New Zealand for the years 1942–61. Origin times only are considered, the energies and exact positions of the shocks being largely ignored. The relevant statistical theory for the first and second order properties of the process is described, and simple probability models for earthquake occurrence are put forward. On the basis of these results, the data are examined for periodic and grouping effects. No significant periodic effects are found, either among the shallow shocks (depths up to 100 km) or among the deep shocks (depths 100 km or greater). Both components show strong evidence of grouping, and several alternative models to describe this effect are put forward and compared.