An Analysis of Panel Count Data from Multiple random processes

An Integer-valued autoregressive integrated (INARI) model is introduced to eliminate stochastic trend and seasonality from time series of count data. This INARI extends the previous integer-valued ARMA model. We show that it is stationary and ergodic to establish asymptotic normality for conditional least squares estimator. Optimal estimating equations are used to reflect categorical and serial correlations arising from panel count data and variations arising from three random processes for obtaining observation into estimation. Under regularity conditions for martingale sequence, we show asymptotic normality for estimators from the estimating equations. Using cancer mortality data provided by the U.S. National Center for Health Statistics (NCHS), we apply our results to estimate the probability of cells classified by 4 causes of death and 6 age groups and to forecast death count of each cell. We also investigate impact of three random processes on estimation.