On the application of integer-valued time series models for the analysis of disease incidence

Abstract

Statistical time series models are practical tools in public health surveillance. Their capacity to forecast future disease incidence values exemplifies their usefulness. Using these forecasts, one can develop strategies to trigger alerts to public health officials when irregular disease incidence values have occurred. Clearly, the better the forecasting performance of the model class used in the time series analysis, the more realistic are the alerts triggered. The time series analysis of disease incidence values has often entailed the Box and Jenkins model class. However, this class was designed to model real‐valued variables whereas disease incidences are integer‐valued variables. A new class of time series models, called integer‐valued autoregressive models, has been developed and studied over the past decade. The objective of this paper is to introduce this new class of models to the application of time series analysis of infectious disease incidence, and to demonstrate its advantages over the class of real‐valued Box and Jenkins models. The paper also presents a bootstrap method developed for the calculation of forecast interval limits. Copyright © 1999 John Wiley & Sons, Ltd.

Estimation and Forecasting in INAR(P) Models Using Sieve Bootstrap

“…In the context of INAR processes, to the best of our knowledge, we found only few papers about bootstrap and INAR(p) model. Cardinal et al (1999) and Kim and Park (2008) propose a bootstrap approach for deriving forecasts and confidence intervals while Kim and Park (2010) apply bootstrap to INAR(p) models to obtain estimated standard errors for the estimated parameters of the model. 1…”

“…By viewing such autoregressive approximations as a sieve for the underlying infinite-order process, the bootstrap procedure may still be regarded as a non parametric one. Cardinal et al (1999) and Kim and Park (2008) employ this approach after some modifications to incorporate the nature of the integer-valued time series.…”

“…Our approach differs from Cardinal et al (1999) and Kim and Park (2008) approach in the computation of the residuals. In particular, these authors compute the residuals as:…”

“…In particular we compare the performance of our bootstrap approach (SB-INAR) with that of the sieve bootstrap of Cardinal et al (1999) and Kim and Park (2008) (SB) and that of block bootstrap (BB). In the simulation study, we generated 1000 different realization from the following DGPs: (i) PoINAR(p) with λ = 1, 5 (ii) INAR(p) with binomial error term (BINAR) with m = 6, π = 0.2, 0.5, 0.8, (iii) INAR(p) with negative binomial error term (NBINAR) with r = 6, π = 0.2, 0.5, 0.8.…”

“…In particular, we propose a new approach based on the sieve bootstrap that allows for the integer nature of data. We compare this approach with that of Cardinal et al (1999) and Kim and Park (2008) that, to the best of our knowledge, are the only attempts to forecast INAR models using bootstrap. In particular, these authors develop a bootstrap method based on sieve bootstrap to calculate forecasts and confidence intervals, yet they fall short from providing simulation results.…”