Related papers: Financial Time Series and Statistical Mechanics
In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as…
We briefly review statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents…
Residual coherence is a graphical tool for selecting potential second-order interaction terms as functions of a single time series and its lags. This paper extends the notion of residual coherence to account for interaction terms of…
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…
Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the…
In [4], we examined the use of coupling to obtain bounds on the mixing time of statistics on Markov chains. In the present paper, we consider the same general problem, but using strong stationary times rather than coupling. We discuss…
Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect…
This article investigates the use of Machine Learning and Deep Learning models in multivariate time series analysis within financial markets. It compares small and big data approaches, focusing on their distinct challenges and the benefits…
The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Financial networks have become extremely useful in characterizing the structure of complex financial systems. Meanwhile, the time evolution property of the stock markets can be described by temporal networks. We utilize the temporal network…
We study the dynamics of the linear and non-linear serial dependencies in financial time series in a rolling window framework. In particular, we focus on the detection of episodes of statistically significant two- and three-point…
We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter $\beta$ that fluctuates on a large time scale as…
In financial time series there are periods in which the value increases or decreases monotonically. We call those periods elemental trends and study the probability distribution of their duration for the indices DJIA, NASDAQ and IPC. It is…
This paper introduces a new framework to quantify distance between finite sets with uncertainty present, where probability distributions determine the locations of individual elements. Combining this with a Bayesian change point detection…
In a continuous time stochastic economy, this paper considers the problem of consumption and investment in a financial market in which the representative investor exhibits a change in the discount rate. The investment opportunities are a…
In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…
In foreign exchange markets monotonic rate changes can be observed in time scale of order of an hour on the days that governmental interventions took place. We estimate the starting time of an intervention using this characteristic behavior…
In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. This tutorial aims to introduce a number of different stochastic processes that can help in grasping the essential…
Recurrent boom-and-bust cycles are a salient feature of economic and financial history. Cycles found in the data are stochastic, often highly persistent, and span substantial fractions of the sample size. We refer to such cycles as "long".…