Financial Time Series Fractalization (from OHLC time series to univariate fractal, Pan, 2006)

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MSDP Models Step 1 Multilevel Fractal
Decomposition

• Financial Time Series Fractalization(from OHLC
  time series to univariate fractal, Pan, 2006)
• A Top-Down Algorithm Time Series
  Generalization(Recursive Line Generalization,
  Duda Hart, 1973 MDL-based line
  generatlization, Pan, 1994)
• A Bottom-Up Algorithm Empirical Mode
  Decomposition (EMD)and Hilbert Spectrum (N.
  Huang et al, 1998, NASA)
• Financially Sensible Feature Extration on
  Multiple Scale Levels(Pan, 2006, ongoing)

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A Top-Down Algorithm for Multilevel Fractal
Decomposition
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Golden Section of Day Session142pm
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Golden Section of Day Session142pm
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
Enter
Stop Loss
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
Enter
Stop Loss
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
Stop Loss
Entry
Initial Stop Loss
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
Target
Stop Loss
Stop Loss
Entry
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A Top-Down Algorithm for Multilevel Fractal
Decomposition
Target
Stop Loss
Stop Loss
Entry
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Log-Periodic Power Laws
Discontinuation of LPPL
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A Bottom-Up Algorithm Empirical Mode
Decomposition(Norden E. Huang et al, NASA, Proc.
Royal Society London A (1998) 454, 903-995)

• Before EMD, available sequential data analysis
  methods
• For Nonstationary (but Linear) time series
• Probability distributions
• Spectral analysis and Spectrogram (Fourier
  transform)
• Wavelet analysis
• Wigner-Ville distributions
• Empirical Orthogonal Functions (aka Singular
  Spectral Analysis)
• Moving averages
• Successive differentiations (Engle-Granger
  co-integration)
• For Nonlinear (but Stationary and Deterministic)
  time series
• Phase space method- Delay reconstruction and
  embedding- Poincaré surface of section-
  Self-similarity, attractor geometry and fractals
• Nonlinear prediction
• Lyapunov exponents for stability

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• Empirical Mode Decomposition (EMD)
• Decomposes non-linear non-stationary time series
  into independent modes (IMF)- Process referred
  to as sifting- Sum of modes return original
  data (mathematically complete)
• Intrinsic Mode Functions (IMF)- Sinusoidal time
  series- Number of extrema number of zero
  crossings 1- Mean value of envelope zero

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• Hilbert Transform
• transform time dependent signal X(t) to Y(t)
• Describes the local behavior of the data sensibly

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• Hilbert-Huang Transform (HHT)
• Combines Empirical Mode Decomposition (EMD) and
  Hilbert transform
• Decomposes time series data into Independent
  Mode Functions (IMF)
• Creates Hilbert Spectrums
• Provides a mathematically complete multilevel
  wave representation of the original time series
  data.

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• Financial Time Series are much more complex than
  physical signals (oceanic waves)
• X(t) (X.open(t), X.high(t), X.low(t), X.close,
  X.volume(t))
• This demands an adaptation of HHT for vector time
  series
• Financial time series are yet to be embedded in
  multivariate economic time series, mixture of
  prescheduled and random events
• There are multilevel seasonalities
• There are multilevel dynamic cycles.