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
- 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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Cites background from "Detecting correlation in stock mark..."
...We are also aware of a stream of work [6, 17 ,8,9] that constructs a weighted graph on time series in order to discover different interesting patterns....
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3 citations
Cites background or methods from "Detecting correlation in stock mark..."
...Among these, Yamashita et al. (2005) applied a multi- branch artificial neural network (MBNN) to financial market applications. After investigating the predictive accuracy of the TOPIX index of the Tokyo Stock market using MBNN, the results evidenced that these multi-branch neural networks based on artificial intelligence might be more capable of generating greater generalization and representation, compared to simple conventional neural networks. Using the index value of TOPIX, multi-branch neural networks are better at predicting the next day TPOIX values. After various simulations were conducted to compare the multi-branch neural networks with other conventional neural networks, it was concluded that investors and economists can achieve a higher accuracy of forecasting with the proposed MBNN model. Moreover, Afolabi and Olatoyosiuse (2007) used the “Kohonen Self Organising Map (SOM) and hybrid Kohonen SOM” prediction of stock prices....
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...Among these, Yamashita et al. (2005) applied a multi- branch artificial neural network (MBNN) to financial market applications....
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...However, the prevalence of complexity in stock market prices made intelligent prediction paradigms highly significant, as well as forecasting stock prices using the conventional prediction models of CAPM and Fama and French (Huang et al., 2004; Wichard et al., 2004)....
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...7 Adaptive Neural Fuzzy Inference Systems Zadeh (1965) introduced fuzzy logic to show and manipulate data and information involving several types of uncertainty....
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1 citations
References
11,507 citations
"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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1,808 citations
"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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...Tp...
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50 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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Frequently Asked Questions (8)
Q2. What is the scheme the authors introduce for market analysis?
The scheme the authors 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)).
Q3. What is the reason why the model is normalized with the variance of the time series?
The modeling error is normalized with the variance of the time series Ri(t) for a simple reason: A value of cp(i, j) ≥ 1.0 indicates that the mean value 〈Ri〉 is a more appropriate model than f(·), which means that there is no linear dependence in the the time series under investigation.
Q4. What is the definition of the cross correlation matrix?
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.
Q5. What is the role of the cross-correlation matrix in portfolio theory?
The analysis of the the cross-correlation matrix of the returns plays an important role in portfolio theory and financial analysis.
Q6. What is the definition of the correlation matrix?
By definition the correlation matrix is symmetric with respect to i and j and thus cannot be used to distinguish a symmetrical interaction between different stocks from an asymmetric one.
Q7. What is the matrix of differences in the mixed state analysis?
For the mixed state analysis the authors use a time lag of τ = 3 and the authors calculate the matrix of the modeling error 1 as defined in equation 2 and further the matrix of differences δ(i, j) from equation 3.
Q8. What is the main idea of the approach?
This approach is based on the reconstruction of mixed states consisting of delayed samples taken from simultaneously measured time series of both systems under investigation.