Open AccessUniversality of delay-time averages for financial time series: analytical results, computer simulations, and analysis of historical stock-market prices
Author(s) -
Stefan Ritschel,
Andrey G. Cherstvy,
Ralf Metzler
Publication year - 2021
Publication title -
journal of physics. complexity
Language(s) - English
Resource type - Journals
ISSN - 2632-072X
DOI - 10.1088/2632-072x/ac2220
Subject(s) - econometrics , stock market , financial market , probabilistic logic , stock market index , geometric brownian motion , economics , time series , universality (dynamical systems) , stock (firearms) , stochastic differential equation , computer science , mathematics , statistical physics , statistics , finance , geology , physics , diffusion process , mechanical engineering , paleontology , economy , horse , service (business) , quantum mechanics , engineering
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.