Levy’s stable distribution for stock crash detecting

Abstract

In this paper we study the possibility of construction indicators-precursors relying on one of the most power-law tailed distributions - Levy’s stable distribution. Here, we apply Levy’s parameters for 29 stock indices for the period from 1 March 2000 to 28 March 2019 daily values and show their effectiveness as indicators of crisis states on the example of Dow Jones Industrial Average index for the period from 2 January 1920 to 2019. In spite of popularity of the Gaussian distribution in financial modeling, we demonstrated that Levy’s stable distribution is more suitable due to its theoretical reasons and analysis results. And finally, we conclude that stability α and skewness β parameters of Levy’s stable distribution which demonstrate characteristic behavior for crash and critical states, can serve as an indicator-precursors of unstable states.

Econophysics of cryptocurrency crashes: an overview

“…Recently, the use of dynamic indicators, precursors of crashes in stock markets using the parameters of a α-stable distribution was proposed by us in the papers [76,77,286] and later repeated in a recent paper [30]. From the data above, we estimate the parameters α and β of the stable distribution that the best describes the empirical returns.…”

“…These studies [74,75] consider that measures of financial and macroeconomic activity can be drivers of Bitcoin returns. Reviewing papers of the researches above, the experience of others and our own [76][77][78][79][80][81][82][83][84][85], we have revised our classification of such leaps and falls, relying on Bitcoin time series during the entire period (01.01.2011-21.01.2021) of verifiable fixed daily values of the Bitcoin price (BTC) (https://finance.yahoo.com/cryptocurrencies). We emphasize that • crashes are short and time-localized drops that last approximately two weeks, with the weighty losing of price each day.…”

Efficiency of Price Movements in Futures Markets

“…When µ < 2, the tail is termed a ‘heavy tail’ and has a theoretically undefined variance. Accurate fitting the tails of this kind of an empirical distribution with a power law is notoriously difficult (Bielinskyi et al, 2019; Rachev et al, 2005; Weron, 2001).…”

Recurrence analysis of innovation behavior of bitcoin market agents in conditions of COVID-19

“…A significant number of scientific and practical works are devoted to the research of time series of cryptocurrencies, carried out by methods of machine learning and forecasting [3,4], nonlinear autoregression [5], binomial logistic regression [6], recurrent neural network, ARIMA model [7], Bayesian neural networks [8], theory of complex systems [9][10][11][12][13], fractal analysis [9,[14][15][16][17][18][19] and others. However, the identification of the behavior of digital economy agents requires a search for specific parameters that would uniquely determine it.…”