Modelling of low count heavy tailed time series data consisting large number of zeros and ones

Raju Maiti (), Atanu Biswas () and Bibhas Chakraborty ()
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Raju Maiti: Duke-NUS Medical School
Atanu Biswas: Indian Statistical Institute
Bibhas Chakraborty: Duke-NUS Medical School

Statistical Methods & Applications, 2018, vol. 27, issue 3, No 3, 407-435

Abstract: Abstract In this paper, we construct a new mixture of geometric INAR(1) process for modeling over-dispersed count time series data, in particular data consisting of large number of zeros and ones. For some real data sets, the existing INAR(1) processes do not fit well, e.g., the geometric INAR(1) process overestimates the number of zero observations and underestimates the one observations, whereas Poisson INAR(1) process underestimates the zero observations and overestimates the one observations. Furthermore, for heavy tails, the PINAR(1) process performs poorly in the tail part. The existing zero-inflated Poisson INAR(1) and compound Poisson INAR(1) processes have the same kind of limitations. In order to remove this problem of under-fitting at one point and over-fitting at others points, we add some extra probability at one in the geometric INAR(1) process and build a new mixture of geometric INAR(1) process. Surprisingly, for some real data sets, it removes the problem of under and over-fitting over all the observations up to a significant extent. We then study the stationarity and ergodicity of the proposed process. Different methods of parameter estimation, namely the Yule-Walker and the quasi-maximum likelihood estimation procedures are discussed and illustrated using some simulation experiments. Furthermore, we discuss the future prediction along with some different forecasting accuracy measures. Two real data sets are analyzed to illustrate the effective use of the proposed model.

Keywords: Geometric INAR (1); Mixture distribution; Strongly stationary; Coherent forecasting; Zero-inflation; Over-dispersion (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10260-017-0413-z

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