Modeling the temporal and spacial dependence structure in earthquake data from different regions in Pakistan

Abstract As Pakistan is situated in earthquake prone area and in the past many destructive earthquakes have occurred including the most destructive 1935 Quetta, and 2005 Kashmir, 2005 earthquakes. It is of vital importance to investigate the statistical properties of the earthquake temporal data of different regions of Pakistan to mitigate earthquake hazard. The present study brings novelty in the field of statistical seismology through the vast extension of the autoregressive conditional duration models. These models are applied to the earthquake temporal data of different seismic zones of Pakistan to facilitate earthquake hazard analysts. Different specifications of the duration models were considered to parsimoniously capture the time dependency structure present in the data. We used the linear Autoregressive Conditional Duration (ACD), logarithmic ACD models, i.e., LACD1 and LACD2, Augmented Box-Cox ACD (ABACD) and Additive and Multiplicative ACD (AMACD) models. These models were applied to the earthquake temporal data of different regions of Pakistan and the most suitable in-sample fitted and out-of-sample forecasted models were chosen through various models evaluation criteria. The obtained results suggest that the simple linear LACD2(1, 1) model appeared as the most suitable model for modeling earthquake temporal data of different zones of Pakistan. Further, the linear ACD(1, 1) models out perform the remaining considered models regarding 1-through-4 steps-ahead out-of-sample forecasting performance for both IEC and MS zones. The Burr and exponential distributions are appeared as the most appropriate error distributions in ACD(1 ,1) model by generating the forecasts for IEC and MS zones respectively. Hence, it is suggested to use the most suitable in-sample fitted LACD2(1, 1) model to parsimoniously capture the dependency structure present in the considered earthquake data of different zones of Pakistan. Further, the most appropriate out-of-sample forecasting ACD(1, 1) model is recommended to be used for forecasting the earthquake temporal data of Pakistan. The obtained results have many useful utilizations in earthquake hazard and risk mitigation studies for Pakistan.