Related papers: Medium and Small Scale Analysis of Financial Data
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
In the context of time-subordinated Brownian motion models, Fourier theory and methodology are proposed to modelling the stochastic distribution of time increments. Gaussian Variance-Mean mixtures and time-subordinated models are reviewed…
We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets: (a) the New York Stock Exchange, (b) the…
This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor…
We present a symmetry analysis of the distribution of variations of different financial indices, by means of a statistical procedure developed by the authors based on a symmetry statistic by Einmahl and Mckeague. We applied this statistical…
This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval {\Delta} results in…
We study the evolution of probability distribution functions of returns, from the tick data of the Korean treasury bond (KTB) futures and the S$&$P 500 stock index, which can be described by means of the Fokker-Planck equation. We show that…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena,…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…
In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…
In this paper we have analyzed scaling properties of time series of stock market indices (SMIs) of developing economies of Western Balkans, and have compared the results we have obtained with the results from more developed economies. We…
Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence), and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the…
Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity,…
We propose a new statistical test to identify non-stationary frequency-modulated stochastic processes from time series data. Our method uses the instantaneous phase as a discriminatory statistics with reliable critical values derived from…