Central Limit Theorem for Autoregressive Integrated Moving Average Processes

摘要

A modification of the classical compound Poisson process has been shown to be aviable model for describing total claims and compensation costs associated with hazardous material exposure. This model assumes that the successive claim awards form an autoregressive integrated moving average (ARIMA) process. In order to make practical approximations to the distribution of total claim and compensation costs with this model, it is necessary to develop approximations to the distribution of the sum of successive elements from an ARIMA process. In this investigation, a central limit theorem is developed for ARIMA processes, that makes this approximation possible in the case where the number of summands is large.... ARIMA Processes, Compound poisson process, Nonhomogeneous poisson process, Claims and compensation costs, Normal approximation, Time series.