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Inference for bivariate integer-valued moving average models based on binomial thinning operation.

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Summary
This summary is machine-generated.

This study introduces Bivariate Integer-valued Moving Average (BINMA) models for analyzing multivariate count time series data. These models address challenges in existing methods, offering a new approach for discrete time series analysis.

Keywords:
Bivariate discrete distributionsbivariate modelsgeneralized method of momentsmoving averagetime series of counts

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Econometrics

Background:

  • Count time series data are prevalent across various scientific disciplines.
  • Existing models for multivariate count time series present significant challenges.
  • The literature lacks detailed methodologies for handling bivariate discrete time series.

Purpose of the Study:

  • To introduce and analyze Bivariate Integer-valued Moving Average (BINMA) models.
  • To investigate the probabilistic and statistical properties of BINMA models.
  • To provide a robust framework for modeling and analyzing bivariate count time series.

Main Methods:

  • Development of BINMA models utilizing binomial thinning.
  • Analysis of two parametric cases: Bivariate Poisson and Bivariate Negative Binomial innovations.
  • Parameter estimation using the Generalized Method of Moments.

Main Results:

  • The study details the probabilistic and statistical characteristics of BINMA models.
  • Parametric models based on Bivariate Poisson and Negative Binomial innovations are explored.
  • The Generalized Method of Moments proves effective for parameter estimation.

Conclusions:

  • BINMA models offer a viable solution for multivariate count time series analysis.
  • The proposed models and estimation methods are validated using both synthetic and real-world data.
  • This work contributes a novel approach to the field of discrete multivariate time series modeling.