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 โstationaryโ by differencing. 3
An ARIMA model can be viewed as a โfilterโ that tries to separate the signal from the noise, and the signal is then extrapolated into the future to obtain forecasts.
9. 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.
9
11. Linear Regression Model
๏
Simple linear regression
๏
Least squares estimator
๏
Single explanatory variable
11
iiiฮตฮฒXฮฑY++=
โข
Classics of technical analysis
โข
Useful as a reference for comparison with nonlinear estimates
12. Linear versus Nonlinear Fit
12
Linear fit does not give random residuals
Nonlinear fit gives random residuals
๏ผ
X
residuals
X
Y
X
residuals
Y
X
13. Square Root Regression
๏
The square-root transformation
13
iiiฮตXฮฒฮฒY++=110
โข
Used to
โข
overcome violations of the homoscedasticity assumption
โข
fit a non-linear relationship
14. Square Root Transformation
14
๏ง
Shape of original relationship
X
b1 > 0
b1 < 0
X
Y
Y
Y
Y XX
๏ง
Relationship when transformed
i1i10iฮตXฮฒฮฒY++=i1i10iฮตXฮฒฮฒY++=
15. Quadratic Regression Model
15
๏ง
where: ฮฒ0 = Y intercept ฮฒ1 = regression coefficient for linear effect of X on Y ฮฒ2 = regression coefficient for quadratic effect on Y ฮตi = random error in Y for observation i
Model form:
iiiiฮตXฮฒXฮฒฮฒY+++=212110
17. Log Transformation
17
๏ง
Original multiplicative model
๏ง
Transformed multiplicative model
iฮฒ1i0iฮตXฮฒY1=i1i10iฮต logX log ฮฒฮฒ log Ylog++=
The Multiplicative Model:
๏ง
Original multiplicative model
๏ง
Transformed exponential model
i2i21i10iฮต ln XฮฒXฮฒฮฒ Yln+++=
The Exponential Model:
iXฮฒXฮฒฮฒiฮตeY2i21i10++=
18. 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
18
npppSMAnMMM)1(1โโโ+++ = ๏
19. History Prophet
๏
Dummy predictor for strategy testing
๏
Predicts every point with its future value
๏
Imitates a โprophetโ knowing the future
๏
Delivers 100% of profitable trades
๏
Explicitly uses forward info
๏
Not suitable for practical trading
๏
Analog of โMaximum Profit Systemโ
19
21. 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
21
22. 22
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