2022/06/01 by Wagner Barreto‐Souza, Sokol Ndreca, Barreto-Souza, Wagner +5 · 1 citation
Computer Science · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2206.00736
openalex publication_date 2022/06/01 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28
We propose a novel class of count time series models alternative to the classic Galton-Watson process with immigration (GWI) and Bernoulli offspring. A new offspring mechanism is developed and its properties are explored. This novel mechanism, called geometric thinning operator, is used to define a class of modified GWI (MGWI) processes, which induces a certain non-linearity to the models. We show that this non-linearity can produce better results in terms of prediction when compared to the linear case commonly considered in the literature. We explore both stationary and non-stationary versions of our MGWI processes. Inference on the model parameters is addressed and the finite-sample behavior of the estimators investigated through Monte Carlo simulations. Two real data sets are analyzed to illustrate the stationary and non-stationary cases and the gain of the non-linearity induced for our method over the existing linear methods. A generalization of the geometric thinning operator and an associated MGWI process are also proposed and motivated for dealing with zero-inflated or zero-deflated count time series data.