Mixed-Stable Models: An Application to High-Frequency Financial Data

The paper extends the study of applying the mixed-stable models to the analysis of large sets of high-frequency financial data. The empirical data under review are the German DAX stock index yearly log-returns series. Mixed-stable models for 29 DAX companies are constructed employing efficient parallel algorithms for the processing of long-term data series. The adequacy of the modeling is verified with the empirical characteristic function goodness-of-fit test. We propose the smart-Delta method for the calculation of the alpha-stable probability density function. We study the impact of the accuracy of the computation of the probability density function and the accuracy of ML-optimization on the results of the modeling and processing time. The obtained mixed-stable parameter estimates can be used for the construction of the optimal asset portfolio.

Automated summary

This paper extends the application of mixed-stable models to the analysis of financial data, using the German DAX stock index as a case study for 29 companies. The study proposes the smart-Delta method for calculating the probability density function, with the obtained parameter estimates being used for constructing optimal asset portfolios. The impact of accuracy in computing the probability density function and ML optimization on modeling results and processing time is also examined.