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  -