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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Mixed-Stable Models: An Application to High-Frequency Financial Data.

Igoris Belovas1, Leonidas Sakalauskas2, Vadimas Starikovičius3

  • 1Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University, LT-04812 Vilnius, Lithuania.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study applies mixed-stable models to analyze German DAX stock index data, developing efficient algorithms and a new calculation method for alpha-stable probability density functions. Results aid in optimal asset portfolio construction.

Keywords:
high-frequency datamixed-stable modelsstock index returns

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Area of Science:

  • Quantitative Finance
  • Statistical Modeling
  • Financial Econometrics

Background:

  • High-frequency financial data analysis presents challenges due to its volume and complexity.
  • Traditional models may not fully capture the stylized facts of financial returns, such as heavy tails and asymmetry.
  • Mixed-stable distributions offer a flexible framework for modeling such data.

Purpose of the Study:

  • To extend the application of mixed-stable models to analyze large datasets of high-frequency financial data.
  • To construct mixed-stable models for German DAX stock index yearly log-returns.
  • To introduce and evaluate a novel method for calculating the alpha-stable probability density function.

Main Methods:

  • Application of mixed-stable models to yearly log-returns of 29 DAX companies.
  • Utilizing efficient parallel algorithms for processing long-term financial data series.
  • Employing the empirical characteristic function goodness-of-fit test for model validation.
  • Proposing the smart-Δ method for calculating the alpha-stable probability density function.
  • Investigating the impact of computational accuracy on modeling outcomes and processing time.

Main Results:

  • Successfully constructed mixed-stable models for DAX 30 companies using parallel algorithms.
  • Validated model adequacy using the empirical characteristic function goodness-of-fit test.
  • Introduced the smart-Δ method for accurate alpha-stable probability density function computation.
  • Quantified the influence of probability density function accuracy and ML-optimization on modeling results and efficiency.

Conclusions:

  • Mixed-stable models are effective for analyzing high-frequency financial data like the DAX index.
  • The smart-Δ method provides an accurate and efficient way to compute alpha-stable densities.
  • Parameter estimates from these models can inform optimal asset portfolio construction.