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A stationary Weibull process and its applications.

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We introduce a new Weibull process for analyzing dependent data, particularly useful for gold price modeling where existing methods fail. This novel approach offers a convenient copula structure for dependence analysis.

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Area of Science:

  • Statistics
  • Econometrics
  • Probability Theory

Background:

  • Existing statistical methods struggle with analyzing dependent data exhibiting zero values, as seen in gold price fluctuations.
  • The need for a flexible model that can accommodate positive probability of zero observations and dependence structures is critical.

Purpose of the Study:

  • To introduce a novel discrete-time, continuous-state-space Markov stationary process with a two-parameter Weibull distribution.
  • To address the limitations of current models in analyzing financial time series data, such as gold prices, which often include zero values.

Main Methods:

  • Development of a new Weibull process incorporating dependent variables and a positive probability of zero values.
  • Derivation of key properties, including the joint cumulative distribution function and its copula structure.
  • Proposal of a profile likelihood method for computing maximum likelihood estimators due to the lack of explicit forms.

Main Results:

  • The proposed Weibull process demonstrates a convenient copula structure, enabling detailed dependence analysis.
  • The profile likelihood method provides a viable approach for estimating model parameters.
  • Application to synthetic and Indian gold price data shows the model's strong fit.

Conclusions:

  • The introduced Weibull process effectively models dependent data with zero values, outperforming existing methods.
  • The model's copula structure facilitates the study of dependence properties in financial data.
  • The proposed estimation method is practical and effective for real-world data analysis.