Modeling zero-inflated and zero-deflated count data time series using the INMA(1) process

Document Type : Original Scientific Paper

Authors

Department of Statistics‎, ‎Yazd University‎, ‎Yazd‎, ‎Iran

Abstract

In the real world‎, ‎we may come across with zero-inflated or zero-deflated count data that have a very short-run autocorrelation‎. ‎Integer-valued moving average processes are suitable for modeling these data‎. ‎In this paper‎, ‎a non-negative integer-valued moving average process of the first order with zero-modified geometric innovations is introduced‎. ‎This model is called zero-modified geometric INMA(1) process which contains geometric INMA(1) process ‎as a particular case‎. ‎Some statistical properties of the process are obtained‎. ‎The parameters of the model are estimated by the Yule-Walker method‎. ‎Then‎, ‎using the simulation study‎, ‎we evaluate the performance of this estimators‎. ‎Finally‎, ‎the model is applied to two examples of real time series of the monthly number of rubella cases and the annually number of earthquakes magnitude 8.0 to 9.9‎. ‎Then‎, ‎we exhibit the ability of the model for fitting and predicting count data with excess and deficit of zeros.

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Al-Osh, M. and Alzaid, A.A. (1988). Integer-valued moving average (INMA) process. Statistical Papers, 2(1):281–300.
Alzaid, A.A. and Al-Osh, M. (1988). First-order integer-valued autoregressive (INAR(1)) process: Distributional and regression properties. Statistica Neerlandica, 42(1):53–61.
Bakouch, H.S., Mohammadpour, M. and Shirozhan, M. (2018). A zero-inflated geometric INAR(1) process with random coefficient. Applications of Mathematics, 63(1):79–105.
Barreto-Souza, W. (2015). Zero-modified geometric INAR(1) process for modeling count time series with deflation or inflation of zeros. Journal of Time Series Analysis, 36(6):839–852.
Bourguinon, M. (2018). Modelling time series of counts with deflation or inflation of zeros. Statistics and Its Interface, 11(4):631–639.
Jazi, M.A., Jones, G. and Lai, C.D. (2012). First order-integer valued AR processes with zero inflated Poisson innovations. Journal of Time Series Analysis, 33(6):954–963.
Kocherlakota, S. and Kocherlakota, K. (1992). Bivariate Discrete Distributions, Statistics: Textbooks and Monographs. New York: Marcel Dekker.
Li, C., Wang, D. and Zhang, H. (2015). First-order mixed integer-valued autoregressive processes with zero-inflated generalized power series innovations. Journal of the Korean Statistical Society, 44(2):232–246.
Mahmoudi, E. and Rostami, A. (2020). First-order integer-valued moving average process with power series innovations. Journal of Statistical Theory and Applications, 19(3):415–431.
McKenzie, E. (1988). Some ARMA models for dependent sequences of Poisson counts. Advances in Applied Probability, 20(4):822–835.
Steutel, F.W. and van Harn, K. (1979). Discrete analogues of self decomposability and stability. The Annals of Probability, 7(5):893–899.
Yu, K. and Zou, H. (2015). The combined Poisson INMA(q) models for time series of counts. Journal of Applied Mathematics, 2015:457842.