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Market Forecasting Algorithms

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.

Example of ARIMA forecast

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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 Best Regression

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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

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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

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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

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b1 > 0

b1 < 0

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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

Logistic Regression

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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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Maximum Profit Simulation

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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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