Universality of delay-time averages for financial time series: analytical results, computer simulations, and analysis of historical stock-market prices

Abstract We analyze historical data of stock-market prices for multiple financial indices using the concept delay-time averaging time series (FTS). The region validity our recent theoretical predictions [Cherstvy A G et al 2017 New J. Phys. 19 063045] standard and delayed time-averaged mean-squared ‘displacements’ (TAMSDs) FTS is extended to all lag times. As first novel element, we perform extensive computer simulations stochastic differential equation describing geometric Brownian motion (GBM) which demonstrate a quantitative agreement with analytical long-term price-evolution in terms TAMSD (for crisis-free times). Secondly, present robust procedure determination model parameters GBM via fitting features dynamics stocks cryptocurrencies. employed single-trajectory-based can serve as predictive tool (proxy) mathematically based assessment rationalization probabilistic trends evolution prices.