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Understanding the volatility correlation behavior

Understanding the volatility correlation behavior. POSTECH Phys.Dep 전우철 , 김승환 05. 08.08. content Econophysics - Econometrics & Econophysics 2. Background - Volatility correlation behavior - economic time series - clinical data(Heartbeat) - climate records

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Understanding the volatility correlation behavior

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  1. Understanding the volatility correlation behavior POSTECH Phys.Dep 전우철, 김승환 05. 08.08

  2. content • Econophysics • - Econometrics & Econophysics • 2. Background - Volatility correlation behavior • - economic time series • - clinical data(Heartbeat) • - climate records • 3. Methodology • - Detrended Fluctuation Analysis(DFA) • - Superposition rule of DFA • 4. Result • - Heartbeat data(HRV), high-frequency foreign exchange rate • - Cross-Correlation function between magnitude signals

  3. 1. Econometrics & Econophysics • Econometrics –Parametric analysis • Econophysics –Non-parametric analysis • for financial time series • Parametric analysis

  4. Non-Parametric analysis Auto-correaltion, Covariance, Entropy measure, distribution function… : statistical property in finance data. normal S&P PRE(1999) Nature (1995) • Common stylized facts in Ecometrics and Econophysics • Long memory property in Volatility • 2. Volatility Clustering • 3. Fat-tail in price fluctuation distribution (kurtosis) • 4. Leverage effect (skewness)

  5. * Volatility in time series

  6. 2. Background • Long memory Volatility correlation in Economics • Modeling and pricing long memory in stock market volatility : T. Bollerslev et al. Journal of Econometrics (1996) • Realized volatility and correlation : T. Anderson and T. Bollerslev(1999) • The detection and estimation of long memory in stochastic volatility : J. Bredit Journal of Econometrics (1998) • Forecasting realized volatility using a long-memory stochastic volatility model: estimation, predictionJournal of Econometrics (2005) Auto-correlation ARCH, GARCH -> FIGARCH, Long memory stochastic volatility model(LMSV)

  7. Long memory Volatility correlation in Heartbeat signal(HRV) • Magnitude and Sign Correlations in Heartbeat Fluctuations PRL 86, 1900 (2001) • Characterization of sleep stages by correlations in the magnitude and sign of Heartbeat Increaments PRE 65, 51908 (2002) • Magnitude and sign scaling in power-law correlated time series Physica A 323, 19(2003) Fig 2. Fig 1. Volatility correlation measure -> nonlinear property and multifractality of HRV

  8. Long memory Volatility correlation in Climatic signal • Long-term correlations and multifractality in surface wind speed Europhys. Lett. 68, 184(2004) • Nonlinear volatility of river flux fluctuation PRE 67, 42101(2003) • Long-term memory : A natural mechanism for the clustering of Extreme events PRL 94, 48701 (2005)

  9. Motivation • Volatility correlation behavior : Short-memory in original signal(x(t)) , Long-memory in volatility signal(|x(t|) - Just empirical results • Volatility correlation relates to nonlinear property of signals. But, the relation between x(t) and |x(t)| signal remains unclear. • We address the problems • The relation between correlation structures of x(t) and |x(t)| • Which correlation structure of x(t) generates volatility correlation behavior

  10. 3. Methodology • Detrended Fluctuation Analysis(DFA) H : Hurst exponent ( 0 < H < 1 ) H < 0.5 : anticorrelated H ~ 0.5 : Uncorrelated H > 0.5 : correlated H ~ 2 – D (fractal dimension)

  11. The superposition rule of DFA In our method X(t)

  12. The relation between x(t)(H < 0.5) and |x(t)|(H > 0.5)

  13. ITL/USD The Out-of-phase correlated signal exhibit volatility correlation behavior for all time scale n

  14. Out-of-phase correlation signal : synchronous increasing or decreasing of fluctuation magnitudes • In-phase correlation signal : asynchronous increasing or decreasing of fluctuation magnitudes The relation between correlation properties of X(t) and |X(t)| can be explained through the time organization of F(n)

  15. 4. Results HRV : 36 healthy and patient www.physionet.org FX : 9 nations Foreign-eXchange rates(FX, 환율) for dollar high-frequency 1996 30min(Olson and Associates) HRV FX

  16. HRV FX

  17. Cross-Correlation function between magnitude signals : Cross-correlation between magnitude signals -1 < C(n) < 1 Out-of-phase correlation C(n) -> 1 : volatility correlation In-phase correlation C(n) -> -1

  18. Cross-correlation C(n) for HRV and FX Stretched exponential function

  19. C(n) of HRV and FX

  20. Conclusion • We find a new type of correlation function(C(n)) • that explain the volatility correlation behavior. • 2. Signals with same correlation properties in |X(t)| • can exhibit different correlation structures according to the • function C(n). • 3.We need to exploit stochastic time series model • and expand multivariate analysis.

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