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Goodness-of-fit test for stochastic processes using even empirical moments statistic.

Katarzyna Maraj-Zygmąt1, Grzegorz Sikora1, Marcin Pitera2

  • 1Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.

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This study presents a new method for distinguishing stochastic processes using even empirical moments. The framework efficiently differentiates finite and infinite moment processes, even when they are similar, and is tested on real-world data.

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Area of Science:

  • Statistics
  • Stochastic Processes
  • Data Analysis

Background:

  • Stochastic processes are fundamental in modeling complex systems.
  • Distinguishing between different types of stochastic processes is crucial for accurate analysis.
  • Existing methods may struggle with closely related or complex process distributions.

Purpose of the Study:

  • Introduce a novel framework for efficient stochastic process discrimination.
  • Develop a test statistic based on even empirical moments.
  • Enable goodness-of-fit statistical testing for processes with stationary increments and finite-moment distributions.

Main Methods:

  • Utilized even empirical moments to construct a generalized test statistic.
  • Extended the time-averaged mean-squared displacement framework.
  • Applied the methodology to discriminate between finite- and infinite-moment processes.

Main Results:

  • The proposed test statistic effectively discriminates between finite- and infinite-moment processes.
  • Demonstrated high discrimination power even for closely related process laws.
  • Successfully applied the framework to analyze real metal price data.

Conclusions:

  • The novel framework offers an efficient and intuitive approach to stochastic process discrimination.
  • The methodology provides a robust tool for goodness-of-fit testing.
  • The approach is applicable to real-world data analysis, enhancing statistical modeling capabilities.