Modified Galton-Watson processes with immigration under an alternative offspring mechanism
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.00736
- arXiv:
- arXiv:2206.00736
- Bibcode:
- 2022arXiv220600736B
- Keywords:
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- Statistics - Methodology;
- Statistics - Applications
- E-Print:
- Paper submitted for publication