On the Maximum of a Bivariate INMA Model with Integer Innovations

Area of Science:

• * Probability and Statistics
• * Time Series Analysis
• * Stochastic Processes

Background:

• * Moving average models are foundational in time series analysis.
• * Understanding the behavior of extreme values in these models is crucial for risk assessment.
• * Bivariate models extend univariate analysis to capture dependencies between variables.

Purpose of the Study:

• * To investigate the limiting distribution of the maximum of a bivariate moving average model.
• * To determine if this distribution belongs to Anderson's class.
• * To analyze the asymptotic independence of the components of the bivariate maximum.

Main Methods:

• * Employing techniques for analyzing the limiting behavior of order statistics.
• * Assuming innovations from Anderson's class for the bivariate distribution.
• * Utilizing binomial thinning to model the impact of innovations.

Main Results:

• * The limiting distribution of the bivariate maximum is shown to be of Anderson's class.
• * Asymptotic independence is established for the components of the bivariate maximum.
• * The findings extend existing results for univariate moving average models.

Conclusions:

• * The study successfully characterizes the limiting distribution of the bivariate maximum.
• * The results confirm the applicability of Anderson's class to these complex models.
• * This research contributes to the theoretical understanding of extreme value behavior in bivariate time series.