TY  - JOUR
A1  - Ritschel, Stefan
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
T1  - Universality of delay-time averages for financial time series
BT  - analytical results, computer simulations, and analysis of historical stock-market prices
JF  - Journal of physics. Complexity
N2  - We analyze historical data of stock-market prices for multiple financial indices using the concept of delay-time averaging for the financial time series (FTS). The region of validity of our recent theoretical predictions [Cherstvy A G et al 2017 New J. Phys. 19 063045] for the standard and delayed time-averaged mean-squared 'displacements' (TAMSDs) of the historical FTS is extended to all lag times. As the first novel element, we perform extensive computer simulations of the stochastic differential equation describing geometric Brownian motion (GBM) which demonstrate a quantitative agreement with the analytical long-term price-evolution predictions in terms of the delayed TAMSD (for all stock-market indices in crisis-free times). Secondly, we present a robust procedure of determination of the model parameters of GBM via fitting the features of the price-evolution dynamics in the FTS for stocks and cryptocurrencies. The employed concept of single-trajectory-based time averaging can serve as a predictive tool (proxy) for a mathematically based assessment and rationalization of probabilistic trends in the evolution of stock-market prices.
KW  - econophysics
KW  - geometric Brownian motion
KW  - time-series analysis
Y1  - 2021
U6  - https://doi.org/10.1088/2632-072X/ac2220
SN  - 2632-072X
VL  - 2
IS  - 4
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Meyer, Philipp
A1  - Aghion, Erez
A1  - Kantz, Holger
T1  - Decomposing the effect of anomalous diffusion enables direct calculation of the Hurst exponent and model classification for single random paths
JF  - Journal of physics / Institute of Physics. A, Mathematical, nuclear and general
N2  - Recently, a large number of research teams from around the world collaborated in the so-called 'anomalous diffusion challenge'. Its aim: to develop and compare new techniques for inferring stochastic models from given unknown time series, and estimate the anomalous diffusion exponent in data. We use various numerical methods to directly obtain this exponent using the path increments, and develop a questionnaire for model selection based on feature analysis of a set of known stochastic processes given as candidates. Here, we present the theoretical background of the automated algorithm which we put for these tasks in the diffusion challenge, as a counter to other pure data-driven approaches.
KW  - time-series analysis
KW  - decomposing anomalous diffusion
KW  - anomalous
KW  - diffusion exponent
KW  - process inference
Y1  - 2022
U6  - https://doi.org/10.1088/1751-8121/ac72d4
SN  - 1751-8113
SN  - 1751-8121
VL  - 55
IS  - 27
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -