Brazilian Journal of Probability and Statistics

Coherent forecasting for over-dispersed time series of count data

Raju Maiti and Atanu Biswas

Full-text: Open access

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.

Article information

Source
Braz. J. Probab. Stat., Volume 29, Number 4 (2015), 747-766.

Dates
Received: October 2013
Accepted: April 2014
First available in Project Euclid: 17 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1442513444

Digital Object Identifier
doi:10.1214/14-BJPS244

Mathematical Reviews number (MathSciNet)
MR3397391

Zentralblatt MATH identifier
1332.62361

Keywords
Coherent forecasting geometric distribution probability generating function

Citation

Maiti, Raju; Biswas, Atanu. Coherent forecasting for over-dispersed time series of count data. Braz. J. Probab. Stat. 29 (2015), no. 4, 747--766. doi:10.1214/14-BJPS244. https://projecteuclid.org/euclid.bjps/1442513444


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References

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