Robust Estimation for Bivariate Poisson INGARCH Models.

Area of Science:

• Statistics
• Econometrics
• Time Series Analysis

Background:

• Integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models are crucial for analyzing count time series data.
• Traditional parameter estimation using the conditional maximum likelihood estimator (CMLE) is susceptible to outliers, potentially compromising model accuracy.
• Robust methods are needed to ensure reliable estimation in the presence of data anomalies.

Purpose of the Study:

• To develop and evaluate a robust parameter estimation method for bivariate Poisson INGARCH models.
• To address the sensitivity of conventional estimators to outliers in count time series.
• To provide a reliable alternative for analyzing count data that may contain extreme values.

Main Methods:

• Introduction of the minimum density power divergence estimator for bivariate Poisson INGARCH models.
• Theoretical demonstration of the estimator's consistency and asymptotic normality under specified conditions.
• Utilizing Monte Carlo simulations to assess the estimator's performance with simulated outlier data.

Main Results:

• The proposed minimum density power divergence estimator demonstrates robustness to outliers in bivariate Poisson INGARCH models.
• Simulation studies confirm the estimator's superior performance compared to traditional methods when outliers are present.
• The estimator's practical utility is illustrated through real-world crime count data analysis.

Conclusions:

• The minimum density power divergence estimator offers a robust and reliable approach for parameter estimation in bivariate Poisson INGARCH models.
• This method enhances the analysis of count time series data, particularly in scenarios with potential outliers.
• The findings support the adoption of robust estimation techniques in econometric and statistical modeling of count data.