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Area of Science:

  • Statistics
  • Econometrics
  • Time Series Analysis

Background:

  • Integer-valued time series models are crucial for analyzing count data.
  • Existing threshold autoregressive models may not fully capture time-varying dynamics and external influences.

Purpose of the Study:

  • To introduce a novel time-varying first-order mixture integer-valued threshold autoregressive process driven by explanatory variables.
  • To investigate the fundamental probabilistic and statistical properties of this new model.
  • To develop and analyze estimation and inference methods for the proposed model.

Main Methods:

  • Derivation of estimators using Conditional Least Squares (CLS) and Conditional Maximum Likelihood (CML) methods.
  • Establishment of asymptotic properties for the CLS estimator.
  • Utilizing CLS and CML score functions for threshold parameter inference.
  • Development of three test statistics to detect piecewise structure and explanatory variables.

Main Results:

  • The paper details the theoretical underpinnings and properties of the proposed model.
  • Estimation and inference procedures are established, including asymptotic properties.
  • Simulation studies validate the model's performance.
  • The model is successfully applied to real-world data on VOW stock trading volumes.

Conclusions:

  • The introduced time-varying integer-valued threshold autoregressive model provides a flexible framework for count time series.
  • The developed estimation and testing procedures are statistically sound and practically applicable.
  • The model demonstrates effectiveness in analyzing financial time series data, such as stock trading volumes.