# Detecting correlation in stock market

## Summary (1 min read)

### 1 Introduction

- , where the brackets indicate the time average over all trading days in the investigated period.
- Following their investigations the authors see strong indications that this asymmetric interaction exists in a way that the dynamics of single stocks are leading the dynamics of others significantly.
- The authors indicate this with a cross modeling scheme which is described in the following section.

### 2 Mixed State Analysis

- For δ(i, j) > 0 the authors have cp(i, j) > cp(j, i) which means that the returns of the i-th stock contain more useful information to model the returns of the j-th stock than the other way around.
- In the terms of synchronization this indicates an asymmetrical coupling strength between the two stocks.

### 3 Numerical Simulations

- The authors investigate 600 trading days of the Dow-Jones Industrial Average (DJIA) between 2-Oct-2000 and 3-Mar-2003.
- For all 30 stocks in the DJIA, the authors build the time series of daily returns and calculate the cross-correlation matrix ρ(i, j) (see equation 1).
- The stocks that behave anti correlated with respect to the index (the blue stripes in the correlation matrix) occur in cp(i, j) with an modeling error near one.
- In the matrix of the error differences δ(i, j) the authors find the amount of asymmetry regarding their mixed state analysis that offers a field of further investigations.
- The next step will be a detailed analysis of the time dependence of these asymmetries an the nonlinear dependencies in the stock market.

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### "Detecting correlation in stock mark..." refers methods in this paper

...The model f(·) is a linear function that is fitted using the standard least squares approach (see for example Hastie et al. (2001)) for multiple linear regression models, i.e. it should minimize the residual sum of squares ∑ t(Ri(t) − f(~Ri,j(t)))2....

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### "Detecting correlation in stock mark..." refers background in this paper

...Mantegna (see Mantegna (1999)) discovered a hierarchical Preprint submitted to Elsevier Science 25 April 2004 organization inside a portfolio of stocks by introducing a metric related to the correlation coefficients....

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...The cross-correlation matrix shows some interesting structures, for example are there obvious clusters, there were described by Mantegna (1999)....

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46 citations

### "Detecting correlation in stock mark..." refers background in this paper

...The scheme we introduce for market analysis is related to the “mixed state analysis” of multivariate time series which was developed to detect weak coupling between dynamical systems in the framework of chaotic synchronization (see Wiesenfeldt et al. (2001))....

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...We build the time series of daily returns Ri(t) = Yi(t + 1)− Yi(t) Yi(t) , wherein Yi(t) denotes the closing-price of the i-th stock at day t....

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