Universality of delay-time averages for financial time series
- 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 aWe 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.…
| Author details: | Stefan Ritschel, Andrey G. CherstvyORCiD, Ralf MetzlerORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1088/2632-072X/ac2220 |
| ISSN: | 2632-072X |
| Title of parent work (English): | Journal of physics. Complexity |
| Subtitle (English): | analytical results, computer simulations, and analysis of historical stock-market prices |
| Publisher: | IOP Publ. Ltd. |
| Place of publishing: | Bristol |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/12/27 |
| Publication year: | 2021 |
| Release date: | 2024/01/12 |
| Tag: | econophysics; geometric Brownian motion; time-series analysis |
| Volume: | 2 |
| Issue: | 4 |
| Article number: | 045003 |
| Number of pages: | 30 |
| Funding institution: | Humboldt University of Berlin; Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [ME 1535/7-1, ME 1535/12-1]; Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej) within an Alexander von Humboldt Polish Honorary Research Scholarship |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Gold Open-Access |
| DOAJ gelistet | |
| License (German): |  CC-BY - Namensnennung 4.0 International |
