A non-linear integer-valued autoregressive model with zero-inflated data series.

Area of Science:

• Statistics
• Time Series Analysis
• Stochastic Processes

Background:

• Count time series data often exhibit excess zeros, posing challenges for standard models.
• Existing models may not adequately capture the complex dynamics of zero-inflated or zero-deflated count data.
• A need exists for flexible models that can accommodate various zero patterns in count time series.

Purpose of the Study:

• Introduce a new non-linear stationary process for count time series.
• Develop a model capable of handling excess zeros (inflation and deflation).
• Investigate parameter estimation methods for the proposed process.

Main Methods:

• The proposed process integrates survival and innovation components.
• The survival component utilizes a generalized zero-modified geometric thinning operator.
• Innovation processes with various probability distributions are explored.
• Conditional maximum likelihood and conditional least squares are used for parameter estimation.

Main Results:

• The new process effectively models time series of counts, including those with excess zeros.
• The model demonstrates flexibility in adjusting to observed zero inflation and deflation.
• Parameter estimation methods are investigated and shown to be applicable.

Conclusions:

• The introduced non-linear stationary process offers a robust framework for count time series analysis.
• The model's adaptability to different zero patterns makes it suitable for diverse real-life applications.
• The study provides practical insights into model fitting and parameter selection for count data.