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November 2015 Coherent forecasting for over-dispersed time series of count data
Raju Maiti, Atanu Biswas
Braz. J. Probab. Stat. 29(4): 747-766 (November 2015). DOI: 10.1214/14-BJPS244

Abstract

In the context of an over-dispersed count time series data on disease incidences, we consider the Geometric integer-valued autoregressive process of order 1 or GINAR(1), which was first introduced by McKenzie (Adv. Appl. Probab. 18 (1986) 679–705) as an analogue of continuous AR(1) process with exponential margin (Adv. Appl. Probab. 12 (1980) 727–745) on the positive support ($\mathbb{R}^{+}$). A strong enthusiasm still persists as it is apparent from Ristić et al. (J. Stat. Plann. Inf. 139 (2009) 2218–2226). Coherent forecasting of Poisson INAR(1) process due to Al-Osh and Alzaid (J. Time Ser. Anal. 8 (1987) 261–275) was studied by Freeland and McCabe (Int. J. Forecast. 20 (2004) 427–434). Here, we study the $h$-step ahead forecasting distribution corresponding to GINAR(1) process in details using probability generating function. Large sample distributions of the conditional least squares estimates of the model parameters are derived. Some numerical study is performed to illustrate the theoretical results.

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Raju Maiti. Atanu Biswas. "Coherent forecasting for over-dispersed time series of count data." Braz. J. Probab. Stat. 29 (4) 747 - 766, November 2015. https://doi.org/10.1214/14-BJPS244

Information

Received: 1 October 2013; Accepted: 1 April 2014; Published: November 2015
First available in Project Euclid: 17 September 2015

zbMATH: 1332.62361
MathSciNet: MR3397391
Digital Object Identifier: 10.1214/14-BJPS244

Rights: Copyright © 2015 Brazilian Statistical Association

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Vol.29 • No. 4 • November 2015
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