1. Quant Trader
Presented by
Quant Trade Technologies, Inc.
Market Forecasting Algorithms

2. Premium selection of algorithms

Self-optimizing ARIMA expert
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Finite Impulse Response Neural Network

Finite State Markov Automation

Stepwise Best Regression
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Square Root Regression

Square Regression

Logistic Regression
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3. ARIMA for time series forecasting
ARIMA models are, in theory, the most general class of models for forecasting a time series which can be made to be “stationary” by differencing. 3
An ARIMA model can be viewed as a “filter” that tries to separate the signal from the noise, and the signal is then extrapolated into the future to obtain forecasts.

4. Example of ARIMA forecast
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5. Self-optimizing ARIMA expert
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Full ARIMA(p,d,q) implementation
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Unlimited order of mixed modeling
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Conditional error estimates
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Chi-square statistics on residuals
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Expert inference for optimal parameters
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Automatic trend adjustments
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Prediction on multiple future horizons
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6. FIR Neural Network
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Finite-Impulse-Response (FIR)
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Optimal selection of filter parameters
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Adaptive neural network training
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Temporal back-propagation algorithm
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7. Finite State Markov Automation
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Market data flow exploration
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Dynamically construct Markov models
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Building state transition graph

Predict future market states
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8. Stepwise Best Regression
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9. Stepwise Regression Algorithm
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Enter and remove predictors, in a stepwise manner, until there is no justifiable reason to enter or remove more.
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At each step, enter or remove a predictor based on partial F-tests.
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Stop when no more predictors can be justifiably entered or removed from the stepwise model.
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10. Linear Regression
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11. Linear Regression Model

Simple linear regression

Least squares estimator
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Single explanatory variable
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iiiεβXαY++=
•
Classics of technical analysis
•
Useful as a reference for comparison with nonlinear estimates

12. Linear versus Nonlinear Fit
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Linear fit does not give random residuals
Nonlinear fit gives random residuals

X
residuals
X
Y
X
residuals
Y
X

13. Square Root Regression

The square-root transformation
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iiiεXββY++=110
•
Used to
•
overcome violations of the homoscedasticity assumption
•
fit a non-linear relationship

14. Square Root Transformation
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
Shape of original relationship
X
b1 > 0
b1 < 0
X
Y
Y
Y
Y XX

Relationship when transformed
i1i10iεXββY++=i1i10iεXββY++=

15. Quadratic Regression Model
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
where: β0 = Y intercept β1 = regression coefficient for linear effect of X on Y β2 = regression coefficient for quadratic effect on Y εi = random error in Y for observation i
Model form:
iiiiεXβXββY+++=212110

16. Logistic Regression
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17. Log Transformation
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
Original multiplicative model

Transformed multiplicative model
iβ1i0iεXβY1=i1i10iε logX log ββ log Ylog++=
The Multiplicative Model:

Original multiplicative model

Transformed exponential model
i2i21i10iε ln XβXββ Yln+++=
The Exponential Model:
iXβXββiεeY2i21i10++=

18. Forecast with average value
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Simple moving average predictor
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Predicted value equal to moving average over previous values

Useful as a reference for comparison with more complex algorithms
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npppSMAnMMM)1(1−−−+++ = 

19. History Prophet
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Dummy predictor for strategy testing
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Predicts every point with its future value
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Imitates a “prophet” knowing the future

Delivers 100% of profitable trades
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Explicitly uses forward info

Not suitable for practical trading

Analog of “Maximum Profit System”
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20. Maximum Profit Simulation
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21. Extensible algorithmic API
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Modular algorithmic server
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Extendable calculation engine
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Real-time C++ core framework
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Open standard development API
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Universal DLL interface

Compatibility with development tools

Multiple sample models
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Pioneers in the fractal exploration of financial markets
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