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An Observation-Driven Random Parameter INAR(1) Model Based on the Poisson Thinning Operator.

Kaizhi Yu1, Tielai Tao1

  • 1School of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China.

Entropy (Basel, Switzerland)
|June 28, 2023
PubMed
Summary
This summary is machine-generated.

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This study introduces a new integer-valued autoregressive time series model with observation-driven parameters. The model

Area of Science:

  • Statistics
  • Time Series Analysis
  • Econometrics

Background:

  • Traditional time series models often assume continuous data.
  • Integer-valued time series present unique modeling challenges.
  • Observation-driven parameter models offer flexibility in capturing dynamic behaviors.

Purpose of the Study:

  • To introduce a novel first-order integer-valued autoregressive (INAR(1)) time series model.
  • To incorporate observation-driven parameters that can follow a random distribution.
  • To theoretically analyze the model's statistical properties and demonstrate its practical utility.

Main Methods:

  • Derivation of the model's ergodicity.
  • Theoretical analysis of point estimation, interval estimation, and parameter testing.
Keywords:
ergodicityinteger-valued time seriesinterval estimationobservation-driventhinning operator

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  • Validation through numerical simulations.
  • Application to real-world datasets.

    • Main Results:

    • The ergodicity of the proposed INAR(1) model is established.
    • Theoretical properties for estimation and hypothesis testing are derived.
    • Numerical simulations confirm the theoretical findings.
    • The model demonstrates effectiveness on empirical data.

    Conclusions:

    • The developed integer-valued autoregressive model with observation-driven parameters is theoretically sound.
    • The model provides a flexible framework for analyzing count time series data.
    • Its practical applicability is validated through real-world case studies.