Stochastic dynamical model for stock-stock correlations

Abstract

We propose a model of coupled random walks for stock-stock correlations. The walks in the model are coupled via a mechanism that the displacement (price change) of each walk (stock) is activated by the price gradients over some underlying network. We assume that the network has two underlying structures, describing the correlations among the stocks of the whole market and among those within individual groups, respectively, each with a coupling parameter controlling the degree of correlation. The model provides the interpretation of the features displayed in the distribution of the eigenvalues for the correlation matrix of real market on the level of time sequences. We verify that such modeling indeed gives good fitting for the market data of US stocks.

A simple and exact Laplacian clustering of complex networking phenomena: Application to gene expression profiles

“…C. Comparison with other methods. We have noted other clustering methods such as coupled two-way clustering (CTWC) analysis (13,14) and the stochastic dynamic model (10), which share the similar objective of clustering as ours. CTWC is an iterative clustering process by looking for pairs of a relatively small subset of samples and genes because the ''signal'' may be masked by the ''noise'' generated by the uncorrelated data.…”

“…Another relevant method is the stochastic model of coupled random walks for stock-stock correlations (10). This model consists of a system of n walks at g different times that corresponds to n samples and g genes, respectively, in microarray data.…”

The coupling analysis of stock market indices based on cross-permutation entropy

“…It has attracted much attention [6][7][8][9][10] on the investigating of methodologies about statistical and nonlinear physics to analyze the financial data, such as random matrix theory [3], the wavelet transform modulus maxima approach [11][12][13], and the phase correlation [14]. Besides, the existence of cross-correlation between different observations is an important feature of market dynamics, and many interesting results have been obtained [15][16][17][18][19][20][21][22][23][24].…”

“…Financial markets can be considered as complex dynamic systems of many complex factors such as nonlinear interaction subsystems [1][2][3][4][5]. It has attracted much attention [6][7][8][9][10] on the investigating of methodologies about statistical and nonlinear physics to analyze the financial data, such as random matrix theory [3], the wavelet transform modulus maxima approach [11][12][13], and the phase correlation [14].…”

Phase Statistics Approach to Time Series Analysis

“…As a result, cross-disciplinary studies on financial systems have attracted much attention in recent decades [24][25][26][27][28]. When considering the issue as a generic time series analysis problem, there have been developments in methodology [24,25,29], such as the method of random matrix [24][25][26] and the wavelet transform modulus maxima approach [29][30][31][32][33][34]. The wavelet analysis has difficulty with its non-adaptive nature, so once the basic wavelet is selected, it is used to analyze all the data.…”