Modeling Capital Markets with Financial Signal processing

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Modeling Capital Markets with Financial Signal
processing

• Bridging
• Technical Analysis Stochastic-Process Modeling
• ( I )

???????, ????????
Harmonic Financial Engineering
2
a step toward
Rational Memory Process Canonical Foundation of
Financial Engineering by Sifeon
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Capturing Movements ofCapital Markets
Example SP 500 Index (US Stock Market)
Time Series of Monthly Return Rates
Dynamics of Time-Series Fluctuation to determine
Growth Path
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Dynamic Analysis ofMarket Movements
Categories of Analyzing Methodologies
Endogenous
Technical Analysis
Stochastic-Process Modeling
Demand-Supply Mechanism
Return-Risk Trade-off
Traditional Financial Analysis
Advanced Financial Engineering
Exogenous
Fundamental Analysis
Inter-Market Analysis
Growth-Value Perspective
Dynamics of Capital Flows
various approaches from different perspectives
and for different purposes
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Part I Elementary Ideas in Technical
Analysis naïve financial signal processing
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Reading Charts ofMarket Movements
Correction (????)
Uncertainty
Momentum
Technical Analysis (????) ??????
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Finding Technical Patterns ofMarket
Demand-Supply
Momentum, Risk Aversion and Bargain
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Technical Analysis asFinancial Signal Processing
Endogenous Market Data
Indicator
Filter
fitting into noises or figuring out
trends or creating cycles ???
Market-Cycle Leading Pattern
Empirical Strategy
Historic Simulation
consistent Cycle-Leading Patterns out there?
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Strength and Weakness ofTechnical Analysis

• Strength Observation Explanation about
  Dynamic Phenomena
• trying to explain filtered patterns
• based on
• market demand-supply mechanism driven by market
  sentiment
• e.g.
• Moving Average (EMA, MACD), Relative Strength
  Index, Money Flow Index,
• Bollinger Bands, Support and Resistance Levels,
• Weakness Formulation Correction about
  Dynamic Structure
• lack of probabilistic formulation
• for
• consistent strategy construction by risk-return
  trade-off
• and
• systematic performance assessment

be aware of noisy illusions!
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Part II Fundamental Structures in
Stochastic-Process Modeling naïve capital
market modeling
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Mathematical Foundation ofFinancial Engineering
Time Series of Periodic Return Rates
Ri (Si-Si-1)/Si-1
Probabilistic Formulation L(Rii1, ) Joint
Distribution
Dynamic Statistics L?(i) (Ri)i1,
Stochastic Evolution
Information Implication L(Si1Si)i1,
Prob. Transition
recognizing the random nature and formalizing the
stochastic structure
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Academic Canonical Frameworks ofCapital Market
Modeling
could the models borrowed from physical systems
well approach econ ones?
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Finding Clues forVerifying Models
dynamic tracing
static de-mixing
just simply a normal distribution or a
complicated mixture of normal distributions?
tractable Dynamic Structure out there?
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Strength and Weakness ofStochastic-Process
Modeling

• Strength Formulation Correction about
  Dynamic Structure
• strong probabilistic formulation
• for
• consistent strategy construction by risk-return
  trade-off
• and
• systematic risk management (tools paradigms by
  financial engineering)
• Weakness Observation Explanation about
  Dynamic Phenomena
• Ignoring (if any) cyclic phenomena and
  investment paradigms
• due to
• market demand-supply mechanism
• driven by
• market sentiment and rationality

be aware of simple biases!
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Part III Reality Lessons its a jungle out
there
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The Complex Reality forThoughts

• Capital Markets are Complex Dynamic Systems
• Non-linear Dynamic Mechanism
• Non-stationary Evolution due to changing Econ
  Conditions and Investment Paradigms
• Multi-Component Framework of Market Behavior
• Trend Change Points, Long-Term Evolutionary
  Structural Changes
• Seasonality Periodic Factors
• Cycles Dynamic Swings around Equilibrium
• Shocks Unpredictable Impacts
• Noises Endogenous and Environmental
  Uncertainties
• Diversification in Market Constitution
• Sentiment Individual Investors
• Rationality Institutional Investors (Smart
  Money)
• Strategy Arbitrageurs, Risk Hedgers
• Multi-Channel Infrastructure of Money Flows
• Swifter and Swifter Trading Systems
• Broader and Broader Asset Categories

can deal with it ???
GARCH
?
?
too many factors affecting market movements to
figure out?!
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Multi-ResolutionofComplex Market Time Series
wavelet-based decomposition to figure out market
behavior features
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Hard Lessons fromMarkets

• 1974 Great Stock Market Capitulation
• 1987 Great Stock Market Crash
• 1989 Nikkei Bubble Burst
• 1997 Asian Currency Crisis
• 1998 LTCM Fallout
• 2000 Nasdaq (Tech) Bubble Burst

dynamic risks beyond interpretation of stochastic
volatility (no anomaly talk)
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Part IV Rational Memory Processes a canonical
methodological framework of capital market
modeling based on financial signal processing
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Prospects forModeling Capital Markets

• Theoretical Issues (about mathematical analysis)
• Dynamics Demand Supply Mechanism
• Randomness Uncertainty Structure (multi-scale
  noise structure)
• Practical Issues (about paradigms)
• Market Sentiment Momentum, Uncertainty
• Market Rationality Prediction, Risk-Return
  Trade-Off
• Market Strategy Arbitrage, Risk Hedging
  Schemes
• Market Efficiency Completeness Financial
  Infrastructures, Products
• Market Liquidity Friction Trading Volumes,
  Cost, Turn-Over rate
• Market Constitution Economical, Cultural,
  Geopolitical Backgrounds
• Technical Issues (about applications and
  implications)
• Model Identification Parameter Estimation
• Model Assessment Modeling Risk (Modeling Bias,
  Estimation Loss)
• Model Adaptation Coefficient Relations to Econ
  and Other Markets Conditions
• Model Extensibility Extension to Absorb New
  Factors counting for Anomalies

setting a modeling methodological framework to
incorporate the prospects
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Challenges forModeling Capital Markets

• Non-linearity Non-stationarity in Signal
  Dynamics
• Complexity in Signal Structure
• Noise Barrier (Overwhelming Noise-to-Signal
  Ratio)
• Nonparametric Estimation (M.L.E. does not make
  sense anymore here)

Piecewise (Monthly) Constant Geometric Brownian
Motion
Ri µ(Ri-1, Ri-2, )s (Ri-1, Ri-2, ) ?ei
Curse of Dimensionality
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Technical FoundationforFinancial Signal
Processing
Analyzing Signals over Fourier Frequency Domain
Complexity in Signal Structure
Analyzing Signals in Wavelet Multi-Resolution
Framework
Non-linearity Non-stationarity in Signal
Dynamics
Analyzing Signals over Dynamic Domain in Wavelet
Multi-Resolution Framework
Transformation Magic to break Curse of
Dimensionality
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Fundamental Signal Processing TasksforFinancial
Engineering
Historic Time Series
Technical Indicator
Filter
Di
S0, S1, , Si
Di ?(S0, , Si V0, , Vi, ...?i)
continuous-time approach
Dt ?t(St0,t)
special interested format
Di ?(R1, , Ri) Rj (Sj-Sj-1)/Sj-1
linear stationary case
Di c1R1 ciRi Dt ?0,tk(t-t)St-1dS
t
an objective way to format market patterns from
experience
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Examples ofDynamic Indicators
Dynamic Indicators Technical Indicators which
serve to monitor and gauge market cycles
Dancing with Cycles
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Critical PatternsofLong-Term Cyclic Phenomena
TAIEX
Nikkei 225
SP 500
12/85
12/90
04/96
04/01
Principle of Cyclic Hazard
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Example IofShort-Horizon Dynamic Patterns
Fidelity Technology Fund (EUR)
Fidelity American Growth Fund (USD)
Index Value
20-Day STTB
08/18/2003
01/20/204
08/18/2003
01/20/204
Fidelity Emerging Markets Fund (USD)
Fidelity World Fund (EUR)
08/18/2003
01/20/204
08/18/2003
01/20/204
catching rebounding points and finding implicit
trend forces
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Example IIofShort-Horizon Dynamic Patterns
20-Day STTB
catching a rebounding and surging point
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Example IIIofShort-Horizon Dynamic Patterns
12-Month M.A. of USD-vs-JPY 12-M STTB
12-Month M.A. of USD-vs-EUR 12-M STTB
12-Month M.A. of USD-vs-JPY Return Rate
12-Month M.A. of USD-vs-EUR Return Rate
Helicoid Pattern of Currency Triangular
Arbitraging
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Example IVofShort-Horizon Dynamic Patterns
5-Day M.A. of TWSEELEC/TWSE Relative 20-Day STTB
5-Day M.A. of TWSEBKI/TWSE Relative 20-Day STTB
TWSEELEC/TWSE Cumulative Relative Return Rate (3)
TWSEBKI/TWSE Cumulative Relative Return Rate (3)
02/13/2003
01/16/2004
Helicoid Pattern of Stock-Index Triangular
Arbitraging
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Conditionsof Modeling Potential

• Physical Meanings
• indicating practical market sense, e.g.
• momentum, uncertainty, stability, liquidity,
  etc.
• Cycle-Leading
• Consistency Universality (Time Geography)

- e.g.
warning markets might have no real intentions,
but filters illusions!
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Constructing Indicator-Oriented Strategieswith
or without Modeling
from empirical to theoretical
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Methodological Framework ofModeling Capital
Markets
Rational Memory Process
Market Aggregation Rationality
Ri1-ri ??(Di) S?(Di)ei1
Market Background Conditions
continuous-time approach (with a linear
stationary filter)
dSt/St ??(?0,tk(t-t)St-1dSt) dt
S?(?0,tk(t-t)St-1dSt)dWt
dynamics based on rationality oriented by memory
filtered by dynamic kernel
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Advantages onDynamic Domain

• neatly constructing dynamic investment
  strategies on the dynamic domain
• analytic calculation of risk-return trade-off
  curve via calculus of variation
• easily formulating integrated-volatility for
• simulating risk-neutral probability density and
  calculating VaR
• turning nonlinear dynamic auto-regression into
• static nonparametric regression
• introducing adaptive statistical estimation
  methods to
• separate stationary and non-stationary factors
• assessing modeling risk
• paving a way to statistical finance (market
  energy)
• keeping the modeling framework flexible and
  adaptive under reflexivity

building robust adaptive models for financial
engineering in magic domains