This document describes market forecasting algorithms provided by Quant Trade Technologies, including self-optimizing ARIMA, finite impulse response neural networks, finite state Markov automation, stepwise best regression, square root regression, logistic regression, and more. It explains the mathematical models behind various linear and nonlinear regression techniques for time series forecasting and analyzing financial market data.

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

2. Premium selection of algorithms

Self-optimizing ARIMA expert

Finite Impulse Response Neural Network

Finite State Markov Automation

Stepwise Best Regression

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

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

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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Quant Trade LLC
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