Intelligent Finance Component II – Multilevel Process Analysis

Second International Workshop on Intelligent Finance (IWIF-II) 6.-8. July 2007, Chengdu, China Intelligent FinanceComponent II – Multilevel Process Analysis Prof Dr PAN Heping, Director of PRC, IIFP, SIIF & SSFI Prediction Research Centre (PRC) University of Electronic Science &Technology of China （UESTC） International Institute for Financial Prediction (IIFP), Finance Research Centre of ChinaSouthwestern University of Finance & Economics (SWUFE) Swingtum Institute of Intelligent Finance (SIIF)Swingtum School of Financial Investment (SSFI) Room 340/306 Yifu Building, Chengdu 610054, China Phone：+8628-83208728, Mobile：13908085966 Email: panhp@uestc.edu.cn, h.pan@iifp.net URL Chinese：www.swingtum.com.cn URL English： www.swingtum.com

Second International Workshop on Intelligent Finance (IWIF-II) 6.-8. July 2007, Chengdu, China Intelligent FinanceComponent II – Multilevel Process Analysis 潘和平（博士、教授、长江学者）电子科技大学预测研究中心主任西南财经大学中国金融研究中心国际金融预测研究所所长形势冲智能金融研究院院长 & 形势冲金融投资学校校长成都市建设北路二段四号逸夫楼340/306 电话：028-83208728, 手机：13908085966 电子邮件: panhp@uestc.edu.cn, h.pan@iifp.net 中文网站：www.形势冲.com, www.swingtum.com.cn 英文网站：www.swingtum.com

Contents • Multilevel Process Analysis (MPA) – Why? How? • Facts and Assumptions underlying MPA • Multilevel Stochastic Dynamic Process Models (MSDP) • Multilevel Fractal Decomposition of Financial Time Series • General Form of MSDP Models • Illustrative Examples of MSDP Models • Multilevel Structural Time Series Models • Multilevel Stochastic Differential Equations • High-level Stochastic Dynamic Process Patterns • Multilevel Log-Periodic Power Laws • Multilevel Dynamic Pattern Recognition for Daily Prediction of Stock Index Returns • Truly Dynamic Prediction Models www.swingtum.com/institute/IWIF

1. Multilevel Process Analysis – Why? How? • Why ?Under the Multilevel Dynamic Market Hypothesis and as a matter of fact, multilevel stochastic dynamic processes of market prices simply exist, and they are either irreducible or not effectively reducible to any single-level process. • How ?Multilevel Stochastic Dynamic Process (MSDP) Models of Financial Time Series- Multilevel Fractal Decomposition of Financial Time Series- Multilevel Structural Time Series Models- Multilevel Stochastic Differential Equations- Multilevel Nonlinear Process Pattern Models- Multilevel Nonparametric Kernel Regression Models- Multilevel Markov Chain of Intermittent Chaos Models www.swingtum.com/institute/IWIF

2. Facts and Assumptions underlying MPA(Dow 1880’s, Graham 1930’s; Elliott 1930’s, Mandelbrot 1970-2004; Peters, 1991; Dacorogna et al, 2001; Pan 2003-2006) • Heterogeneous Market Hypothesis: Market participants are not homogeneous; there are producers, hedgers, investors, traders and speculators; different participants react to the same information in different ways with these characteristics:- Different participants have different time horizons and dealing frequencies;- Different participants are likely to settle for different prices and decide to execute their transactions in different situations, so they create volatility;- The market is also heterogeneous in industrial and financial sectors and in the geographic location of the participants. • Fractal Market Hypothesis: Different participants with different time horizons and dealing frequencies share the same human nature, consequently the market prices exhibit a fractal structure. • Multilevel Dynamic Market Hypothesis: (Swingtum Market Hypothesis)The fractal market prices exhibit robust stochastic dynamic patterns in the scale space of time and price, which can be described in terms of multilevel trends, swings and momentums. www.swingtum.com/institute/IWIF

3. Multilevel Stochastic Dynamic Process Models • Multilevel Fractal Decomposition of Time Series • General Form of Multilevel Stochastic Dynamic Process (MSDP) Models • Multilevel Structural Time Series (MSTS) Models • Multilevel Stochastic Differential Equations (MSDE) • High-Level Dynamic Process Patterns • Multilevel Log-Periodic Power Laws • Multilevel Dynamic Pattern Recognitionfor Daily Prediction of Stock Index Returns www.swingtum.com/institute/IWIF

4. Multilevel Fractal Decomposition of Financial Time Series There are three possible approaches: • Multilevel Fractal Extraction with Geometrical Ratio Series(Multilevel Zigzag Transformation using Fibonnaci Ratios)[0.6180, 0.3820, 0.2361, 0.1459, 0.0902, 0.0557, 0.0344, 0.0213, 0.0132] • Multilevel Top-Down Time Series Generalization(adapted from Duda & Hart, 1960’s, and Pan & Förstner 1991) • Multilevel Bottom Up Empirical Mode Decomposition (EMD)(Hilbert-Huang Transform, 1998) www.swingtum.com/institute/IWIF

Multilevel Fractal Extraction with Geometrical Ratio Series (ratio = 0.618-0.382-0.236) www.swingtum.com/institute/IWIF

Multilevel Fractal Extraction with Geometrical Ratio Series (ratio = 0.1459) www.swingtum.com/institute/IWIF

Multilevel Top-Down Generalization (iteration 1) www.swingtum.com/institute/IWIF

5. General Form of Stochastic Dynamic Process (MSDP) Models www.swingtum.com/institute/IWIF

6. Illustrative Examples of MSDP Models …… www.swingtum.com/institute/IWIF

An Illustrative Example of MSDP Models …… www.swingtum.com/institute/IWIF

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with 1% Brownian motion added www.swingtum.com/institute/IWIF

A Primary Trend of Dow www.swingtum.com/institute/IWIF

Secondary Trends of Dow www.swingtum.com/institute/IWIF

Minor Trends of Dow www.swingtum.com/institute/IWIF

The Elliott Wave Fractal Pattern 5 B 3 A C 4 1 Waves 1, 3, and 5 are impulsive waves.Waves 2 and 4 are corrective waves.Waves A,B,C correct the main trend from wave 1 to wave 5. 2 www.swingtum.com/institute/IWIF

The Elliott Wave Fractal Pattern 5 b 3 a c 4 1 Waves 1, 3, and 5 are impulsive waves.Waves 2 and 4 are corrective waves.Waves a, b, c correct the main trend from wave 1 to wave 5. 2 www.swingtum.com/institute/IWIF

The Elliott Wave Rules and Retracement Ratios 5 b 3 a c 4 1 38.2% 50% 2 61.8% www.swingtum.com/institute/IWIF

7. Multilevel Structural Time Series (MSTS) Models(using P. Young’s Dynamic Harmonic Regression as a Kernel) www.swingtum.com/institute/IWIF

8. Multilevel Stochastic Differential Equations(an illustrative form only) www.swingtum.com/institute/IWIF

A Dynamical Microeconomic Model of Caginalp and Balenovich (2003) Classical theory of adjustment: stipulates that relative price change occurs in order to restore a balance between supply S and demand D, which in turn depend on price with Augmentation by Caginalp and Balenovich (2003): supply and demand depend not only on price, but also on price derivative, so oscillations are introduced. www.swingtum.com/institute/IWIF

and Assume a single group of traders with the total assets limited and normalized to 1 = B (in stocks) + (1-B) (in cash). Let k be the probability or rate at which cash flows into stock. An analysis of asset flow on the conservation of the total capital implies A specific form of the price equation www.swingtum.com/institute/IWIF

Probability k [0, 1] is a function of the total investor sentiment ζ(-∞, +∞) which is the sum of ζ1 the trend-based preference and ζ2 the value-based preference. Let Pa denote the fundamental value, q the amplitude, c a measure of the time scale or “memory length” of the trend (or the value). ζ1 and ζ2 can be expressed as EMA of the trend and the relative discount of the value. and www.swingtum.com/institute/IWIF

and Differentiating ζ1 and ζ2 A Simpler Model in the Long Time Scale Limit:Let c1 and c2 approach 0, d1 = c1q1, d2 = c2q2 and www.swingtum.com/institute/IWIF

A Multilevel Differential Equation Model of Pricesusing Caginalp-Balenovich model as a kernel (for illustration only) e.g. Let with www.swingtum.com/institute/IWIF

Simulation: Level 0 = Line, Level 1 = Sine, Level 2 = Kernel The Result is no longer regular, though using ODE www.swingtum.com/institute/IWIF

9. High-Level Stochastic Dynamic Process Patterns • Turbulence in Forex Markets (Fokker-Planck PDE)(p – probability) • Convergence of Multilevel Trends • Coincidence of Multilevel Cycles and Seasonality • Log-Periodic Power Laws www.swingtum.com/institute/IWIF

10. Multilevel Log-Periodic Power Laws A single-level (mother) log-periodic power law ( Sornette et al, 1996-) An augmented LPPL (Zhou and Sornette, 2003) www.swingtum.com/institute/IWIF

Multilevel Log-Periodic Power Lawsusing Sornette LPPL as a kernel A series of intermediate bottoms (b) and tops (c) Upward Log-Periodic Power Laws Downward Log-Periodic Power Laws www.swingtum.com/institute/IWIF

11. Multilevel Dynamic Pattern Recognition for Daily Prediction of Stock Index Returns www.swingtum.com/institute/IWIF

Intelligent Finance Component II – Multilevel Process Analysis