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

Abstract

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-Δ method for the calculation of the α-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.

Bayesian inversion with α-stable priors

“…First, we can obtain crude uniform bounds (with respect to r) for each (f T ) (i,j) by e.g. differentiating (10) under the integral sign and eliminating the resulting oscillatory term simply using the triangle inequality. We can somewhat refine this pointwise for 'moderate' r > 1 by using standard oscillatory integral techniques (which basically amount to partial integration against a sufficiently quickly vanishing function, resulting in an upper bound of order r −1 ).…”

“…We divide the domain [0, 1.0] × [0.5, 1.9] uniformly to the intervals of h r = 0.01 and h α = 5 • 10 −4 , and evaluate numerically the densities using the integral methods. For the onedimensional α-stable density we use the Fourier integral formula from (10) for |α − 1| < 0.2, and otherwise we employ Nolan's method of (11). Instead of introducing improvised heuristics for the integration and domain partitioning, we count on the Fourier integral for the aforementioned stability values that are particularly tricky in Nolan's method.…”

“…We note that traditionally, stable distributions have been employed in financial applications like the modeling of asset time series [10]. They have also been used in biomedical engineering [11], remote sensing [12], network traffic statistical analysis [13], and digital signal processing [14], to name a few.…”

Comparative analysis of stock price ARIMA and LSTM forecasting methods

“…Lietuvoje, kaip rodo Lietuvos akademinė elektroninė biblioteka eLABa, šios srities tyrimai vykdomi mažesniu intensyvumu. Iš naujesnių publikacijų galima pažymėti Gasparėnienės et al [6] (nagrinėjamos aukso kainos tendencijų prognozės; skaičiavimai parodė, kad ARIMA modelis tinka tik trumpalaikėms aukso kainų prognozėms (ne daugiau kaip 1 metai)), Česnavičiaus [4] (darbe pristatoma ARIMA modeliu paremta Lietuvos elektros energijos kainos prognozė), Belovo et al [1,3]. Nors nuo 2015 m. kainų prognozavimo tematikoje buvo apginta nemažai (dešimtys) bakalauro ir magistro baigiamųjų darbų, daktaro disertacijos buvo apgintos tik dvi [7,15].…”