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Intrinsic Multi-Scale Dynamic Behaviors of Complex Financial Systems.

Ouyang FY, Zheng B, Jiang XF - PLoS ONE (2015)

Bottom Line: However, the cross-correlation between individual stocks and the return-volatility correlation are time scale dependent.The structure of business sectors is mainly governed by the fast mode when returns are sampled at a couple of days, while by the medium mode when returns are sampled at dozens of days.More importantly, the leverage and anti-leverage effects are dominated by the medium mode.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Zhejiang University, Hangzhou 310027, China; School of Electronics and Information, Zhejiang University of Media and Communications, Hangzhou 310018, China; Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China.

ABSTRACT
The empirical mode decomposition is applied to analyze the intrinsic multi-scale dynamic behaviors of complex financial systems. In this approach, the time series of the price returns of each stock is decomposed into a small number of intrinsic mode functions, which represent the price motion from high frequency to low frequency. These intrinsic mode functions are then grouped into three modes, i.e., the fast mode, medium mode and slow mode. The probability distribution of returns and auto-correlation of volatilities for the fast and medium modes exhibit similar behaviors as those of the full time series, i.e., these characteristics are rather robust in multi time scale. However, the cross-correlation between individual stocks and the return-volatility correlation are time scale dependent. The structure of business sectors is mainly governed by the fast mode when returns are sampled at a couple of days, while by the medium mode when returns are sampled at dozens of days. More importantly, the leverage and anti-leverage effects are dominated by the medium mode.

No MeSH data available.


The time series of returns for the German DAX index, and the first ten IMFs decomposed with the EMD method.The left graph describes the 1st IMF to the 5th IMF from top to bottom, and the right one displays the 6th to 10th IMFs from top to bottom.
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pone.0139420.g001: The time series of returns for the German DAX index, and the first ten IMFs decomposed with the EMD method.The left graph describes the 1st IMF to the 5th IMF from top to bottom, and the right one displays the 6th to 10th IMFs from top to bottom.

Mentions: In this section, we analyze the probability distribution of returns, auto-correlation of volatilities and persistence probability of volatilities. We denote the price of a stock index at time t′ as P(t′), then its logarithmic price return over a time interval Δt is defined byR(t′,Δt)≡lnP(t′+Δt)-lnP(t′).(1)△t is first set to be one day, and the effect of different △t will be investigated in the last subsection. To ensure that the results are independent of the fluctuation scales of different financial indices, we introduce the normalized price returnr(t′)=(R(t′)-〈R〉)/σ,(2)where 〈⋯〉 represents the time average over time t′, and is the standard deviation of R(t′) [7]. With the EMD method [35, 36, 38], the time series of the price returns of each financial index is decomposed into a small number of intrinsic mode functions, i.e., the so-called IMFs, which are derived based on the local characteristic time scale of the data itself and characterize the price motion from high frequency to low frequency. But the IMFs are not exact periodic functions, and the cycle and amplitude of each IMF fluctuate within a certain range during the time evolution. To be clearer, we take the German DAX as an example. The time series of returns for this index is decomposed into thirteen IMFs from high frequency to low frequency. In Fig 1, the first ten IMFs are displayed. We observe that the average amplitude of an IMF monotonously decreases from high frequency to low frequency. The average cycle of each IMF is then computed [38]. For the first three IMFs, the cycles are 2.9, 5.5 and 9.4 days, respectively. For the fourth to the eighth IMFs, the cycles are respectively 16.5, 31.4, 59.9, 118.2 and 217.6 days. Roughly, the average cycle obeys a double increase from high frequency to low frequency.


Intrinsic Multi-Scale Dynamic Behaviors of Complex Financial Systems.

Ouyang FY, Zheng B, Jiang XF - PLoS ONE (2015)

The time series of returns for the German DAX index, and the first ten IMFs decomposed with the EMD method.The left graph describes the 1st IMF to the 5th IMF from top to bottom, and the right one displays the 6th to 10th IMFs from top to bottom.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4591268&req=5

pone.0139420.g001: The time series of returns for the German DAX index, and the first ten IMFs decomposed with the EMD method.The left graph describes the 1st IMF to the 5th IMF from top to bottom, and the right one displays the 6th to 10th IMFs from top to bottom.
Mentions: In this section, we analyze the probability distribution of returns, auto-correlation of volatilities and persistence probability of volatilities. We denote the price of a stock index at time t′ as P(t′), then its logarithmic price return over a time interval Δt is defined byR(t′,Δt)≡lnP(t′+Δt)-lnP(t′).(1)△t is first set to be one day, and the effect of different △t will be investigated in the last subsection. To ensure that the results are independent of the fluctuation scales of different financial indices, we introduce the normalized price returnr(t′)=(R(t′)-〈R〉)/σ,(2)where 〈⋯〉 represents the time average over time t′, and is the standard deviation of R(t′) [7]. With the EMD method [35, 36, 38], the time series of the price returns of each financial index is decomposed into a small number of intrinsic mode functions, i.e., the so-called IMFs, which are derived based on the local characteristic time scale of the data itself and characterize the price motion from high frequency to low frequency. But the IMFs are not exact periodic functions, and the cycle and amplitude of each IMF fluctuate within a certain range during the time evolution. To be clearer, we take the German DAX as an example. The time series of returns for this index is decomposed into thirteen IMFs from high frequency to low frequency. In Fig 1, the first ten IMFs are displayed. We observe that the average amplitude of an IMF monotonously decreases from high frequency to low frequency. The average cycle of each IMF is then computed [38]. For the first three IMFs, the cycles are 2.9, 5.5 and 9.4 days, respectively. For the fourth to the eighth IMFs, the cycles are respectively 16.5, 31.4, 59.9, 118.2 and 217.6 days. Roughly, the average cycle obeys a double increase from high frequency to low frequency.

Bottom Line: However, the cross-correlation between individual stocks and the return-volatility correlation are time scale dependent.The structure of business sectors is mainly governed by the fast mode when returns are sampled at a couple of days, while by the medium mode when returns are sampled at dozens of days.More importantly, the leverage and anti-leverage effects are dominated by the medium mode.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Zhejiang University, Hangzhou 310027, China; School of Electronics and Information, Zhejiang University of Media and Communications, Hangzhou 310018, China; Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China.

ABSTRACT
The empirical mode decomposition is applied to analyze the intrinsic multi-scale dynamic behaviors of complex financial systems. In this approach, the time series of the price returns of each stock is decomposed into a small number of intrinsic mode functions, which represent the price motion from high frequency to low frequency. These intrinsic mode functions are then grouped into three modes, i.e., the fast mode, medium mode and slow mode. The probability distribution of returns and auto-correlation of volatilities for the fast and medium modes exhibit similar behaviors as those of the full time series, i.e., these characteristics are rather robust in multi time scale. However, the cross-correlation between individual stocks and the return-volatility correlation are time scale dependent. The structure of business sectors is mainly governed by the fast mode when returns are sampled at a couple of days, while by the medium mode when returns are sampled at dozens of days. More importantly, the leverage and anti-leverage effects are dominated by the medium mode.

No MeSH data available.