Forecasting overdispersed INAR(1) count time series with negative binomial marginal

Abstract

This paper addresses the coherent forecasting problem for overdispersed integer-valued autoregressive (INAR) model of order one having negative binomial marginal distribution. INAR models with Poisson or geometric marginal distribution have been used by several researchers to tackle the forecasting and related issues in low count time series. However, when the process results in relatively higher counts with overdispersion, these models do not provide satisfactory fit and good forecasts. We use negative binomial INAR(1) (NBINAR(1)) model for forecasting the count time series by deriving its exact forecast distribution. Extensive simulation study has been carried out to assess the performance of the forecasts obtained using NBINAR(1) with its INAR(1) counterparts. Two real data sets have been analyzed using the proposed methodology.

Keywords:

• Coherent forecasting
• Geometric distribution
• Integer autoregressive models
• Negative binomial distribution
• Negative binomial thinning

Acknowledgments

Authors are thankful to the editor and reviewers for their suggestions, which has improved the paper substantially.

Additional information

Funding

Manik Awale would like to acknowledge ASPIRE research grant [18TEC001283] from the Savitribai Phule Pune University, Pune. The research of Akanksha S. Kashikar was supported in part by a MATRICS grant [MTR/2017/000729] from DST-SERB, Govt. of India. T. V. Ramanathan’s research was partially supported by a grant from the Department of Science and Technology (DST), Government of India, SR/S4/MS-866/13.