Related papers: A multivariate multifractal model for return fluct…
We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima…
A new class of one-dimensional, discrete time random walk model with memory, termed "Random walk with $n$ memory channels" (RW$n$MC) is proposed. In this model the information of $n$ ($n\in \mathbb{Z}$) previous steps from the walker's…
Financial time series have historically been assumed to be a martingale process under the Random Walk hypothesis. Instead of making investment decisions using the raw prices alone, various multimodal pattern matching algorithms have been…
We discuss the origin of multiscaling in financial time-series and investigate how to best quantify it. Our methodology consists in separating the different sources of measured multifractality by analysing the multi/uni-scaling behaviour of…
It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average…
Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modeling approach is known not to be able to reproduce some of the financial stylized facts, including the dynamics of volatility. In the mathematical…
We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker-Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions…
Vertex-Reinforced Random Walk (VRRW), defined by Pemantle (1988a), is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on arbitrary graphs and show that on…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
The present article explores the application of randomized control techniques in empirical asset pricing and performance evaluation. It introduces geometric random walks, a class of Markov chain Monte Carlo methods, to construct flexible…
By adopting Multifractal detrended fluctuation (MF-DFA) analysis methods, the multifractal nature is revealed in the high-frequency data of two typical indexes, the Shanghai Stock Exchange Composite 180 Index (SH180) and the Shenzhen Stock…
Obtaining reliable estimates of conditional covariance matrices is an important task of heteroskedastic multivariate time series. In portfolio optimization and financial risk management, it is crucial to provide measures of uncertainty and…
Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe…
The elephant random walk (ERW) is a microscopic, one-dimensional, discrete-time, non-Markovian random walk, which can lead to anomalous diffusion due to memory effects. In this study, I propose a multi-dimensional generalization in which…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
We explore the fractional advection-diffusion equation and rare events associated with the ACTRW model. When waiting times have a finite mean but infinite variance, and the displacements follow a narrow distribution, the fractional operator…
In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…
We analyze generalized space-time fractional motions on undirected networks and lattices. The continuous-time random walk (CTRW) approach of Montroll and Weiss is employed to subordinate a space fractional walk to a generalization of the…