Comparison of estimation and prediction methods for a zero-inflated geometric INAR(1) process with random...

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Count time series data often exhibit overdispersion, excess zeros, and autocorrelation, necessitating specialized models.
• Zero-inflated models are crucial for accurately analyzing such data, particularly in fields like ecology and finance.
• The $$ process, a first-order stationary integer-valued autoregressive model with random coefficients and a zero-inflated geometric distribution, presents unique analytical challenges.

Purpose of the Study:

• To investigate and compare various parameter estimation techniques for the $$ process.
• To propose and evaluate novel forecasting methods for zero-inflated count time series.
• To assess the practical performance of different estimation and prediction strategies using simulations and real-world data.

Main Methods:

• Parameter estimation using Whittle, Taper Spectral Whittle, Maximum Empirical Likelihood, and Sieve Bootstrap estimators.
• Forecasting via median, Bayesian, and Sieve Bootstrap prediction methods.
• Performance evaluation through extensive simulation studies and analysis of empirical datasets.

Main Results:

• All investigated estimation and prediction methods demonstrated good performance.
• The 95% highest predicted probability intervals effectively encompassed the observed data across methods.
• Bayesian and Sieve Bootstrap forecasting methods exhibited superior predictive accuracy, justifying their computational cost.

Conclusions:

• The $$ process is amenable to various statistical estimation techniques.
• Bayesian and Sieve Bootstrap methods are recommended for accurate forecasting of zero-inflated count time series.
• The choice of method involves a trade-off between computational efficiency and predictive precision.