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In order to figure out and to forecast the emergence phenomena of social systems, we propose several probabilistic models for the analysis of financial markets, especially around a crisis. We first attempt to visualize the collective…
The financial markets are understood as complex dynamical systems whose dynamics is analysed mostly using nonstationary and brief data sets that usually come from stock markets. For such data sets, a reliable method of analysis is based on…
We address the question of how stock prices respond to changes in demand. We quantify the relations between price change $G$ over a time interval $\Delta t$ and two different measures of demand fluctuations: (a) $\Phi$, defined as the…
We study the volatility of the MIB30-stock-index high-frequency data from November 28, 1994 through September 15, 1995. Our aim is to empirically characterize the volatility random walk in the framework of continuous-time finance. To this…
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given…
A detailed analysis of correlation between stock returns at high frequency is compared with simple models of random walks. We focus in particular on the dependence of correlations on time scales - the so-called Epps effect. This provides a…
This paper is intended as an investigation of the statistical properties of {\it absolute log-returns}, defined as the absolute value of the logarithmic price change, for the Nikkei 225 index in the 28-year period from January 4, 1975 to…
We present a comparative analysis of multifractal properties of financial time series built on stock indices from developing (WIG) and developed (S&P500) financial markets. It is shown how the multifractal image of the market is altered…
Multiplicative cascades have been used in turbulence to generate fields with multifractal statistics and long-range correlations. Examples of continuous and causal stochastic processes which generate such a random field have been carefully…
Time series forecasting is crucial for decision-making across various domains, particularly in financial markets where stock prices exhibit complex and non-linear behaviors. Accurately predicting future price movements is challenging due to…
Great research efforts have been devoted to exploiting deep neural networks in stock prediction. While long-range dependencies and chaotic property are still two major issues that lower the performance of state-of-the-art deep learning…
Stock market indices are volatile by nature, and sudden shocks are known to affect volatility patterns. The autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models neglect structural breaks triggered by…
In this Letter, the dynamic phase transitions of the time-dependent Ginzburg-Landau equations are analyzed using a newly developed dynamic transition theory and a new classification scheme of dynamics phase transitions. First, we…
We propose a novel estimation procedure for scale-by-scale lead-lag relationships of financial assets observed at high-frequency in a non-synchronous manner. The proposed estimation procedure does not require any interpolation processing of…
Intertrade duration of equities is an important financial measure characterizing the trading activities, which is defined as the waiting time between successive trades of an equity. Using the ultrahigh-frequency data of a liquid Chinese…
Stochastic clocks represent a class of time change methods for incorporating trading activity into continuous-time financial models, with the ability to deal with typical asymmetrical and tail risks in financial returns. In this paper we…
This work presents an introduction to feature-based time-series analysis. The time series as a data type is first described, along with an overview of the interdisciplinary time-series analysis literature. I then summarize the range of…
It has been demonstrated recently that supercooled liquids sharing simple structural features (e.g. pair distribution functions) may exhibit strikingly distinct dynamical behavior. Here we show that a more subtle structural feature…
We model time series of VIX (monthly average) and monthly stock index returns. We use log-Heston model: logarithm of VIX is modeled as an autoregression of order 1. Our main insight is that normalizing monthly stock index returns (dividing…
Modelling accurately financial price variations is an essential step underlying portfolio allocation optimization, derivative pricing and hedging, fund management and trading. The observed complex price fluctuations guide and constraint our…