Quant Trader Algorithms
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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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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.
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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.
Self-optimizing ARIMA expert
Full ARIMA(p,d,q) implementation Unlimited order of mixed modeling Conditional error estimates Chi-square statistics on residuals Expert inference for optimal parameters Automatic trend adjustments Prediction on multiple future horizons
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FIR Neural Network Finite-Impulse-Response (FIR) Optimal selection of filter parameters Adaptive neural network training Temporal back-propagation algorithm
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Finite State Markov Automation
Market data flow exploration Dynamically construct Markov models Building state transition graph Predict future market states
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Stepwise Regression Algorithm Enter and remove predictors, in a
stepwise manner, until there is no justifiable reason to enter or remove more.
At each step, enter or remove a predictor based on partial F-tests.
Stop when no more predictors can be justifiably entered or removed from the stepwise model.
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Linear Regression Model Simple linear regression Least squares estimator Single explanatory variable
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iii εβXαY ++=
• Classics of technical analysis • Useful as a reference for comparison
with nonlinear estimates
Linear versus Nonlinear Fit
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Linear fit does not give random residuals
Nonlinear fit gives random residuals
X
resi
dual
s
X
Y
X
resi
dual
s
Y
X
Square Root Regression The square-root transformation
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iii εXββY ++= 110
• Used to • overcome violations of the
homoscedasticity assumption • fit a non-linear relationship
Square Root Transformation
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Shape of original relationship
X
b1 > 0
b1 < 0
X
Y
Y
Y
Y
X
X
Relationship when transformed i1i10i εXββY ++=i1i10i εXββY ++=
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:
iiii εXβXββY +++= 212110
Log Transformation
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Original multiplicative model Transformed multiplicative model
iβ1i0i εXβY 1= i1i10i ε logX log ββ log Ylog ++=
The Multiplicative Model:
Original multiplicative model Transformed exponential model
i2i21i10i ε ln XβXββ Yln +++=
The Exponential Model:
iXβXββ
i εeY 2i21i10 ++=
Forecast with average value
Simple moving average predictor Predicted value equal to moving
average over previous values Useful as a reference for comparison
with more complex algorithms
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nppp
SMA nMMM )1(1 −−− +++=
History Prophet
Dummy predictor for strategy testing Predicts every point with its future value Imitates a “prophet” knowing the future Delivers 100% of profitable trades Explicitly uses forward info Not suitable for practical trading Analog of “Maximum Profit System”
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Extensible algorithmic API
Modular algorithmic server Extendable calculation engine Real-time C++ core framework Open standard development API 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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