Theta Methods

Decomposition-based forecasting. Known for winning the M3 forecasting competition.

Model	Description
Theta	Classic Theta method
AutoTheta	Automatic Theta with optimized parameters
OptimizedTheta	Theta with optimized decomposition parameters
DynamicTheta	Theta with time-varying parameters
DynamicOptimizedTheta	Dynamic + optimized Theta
ThetaX	Theta with exogenous variables

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Theta

Classic Theta method that decomposes series into two theta lines and extrapolates.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period

Example

SELECT * FROM ts_forecast_by(
    'sales_data', NULL, date, sales,
    'Theta', 14, '1d',
    MAP{}
);

Best for: Short-term forecasts, simple + fast, competition-winning accuracy.

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AutoTheta

Automatic Theta method with optimized parameters.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period

Example

SELECT * FROM ts_forecast_by(
    'sales_data', NULL, date, sales,
    'AutoTheta', 14, '1d',
    MAP{}
);

Best for: Short-term forecasts with automatic optimization.

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OptimizedTheta

Theta method with optimized decomposition parameters.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period

Example

SELECT * FROM ts_forecast_by(
    'sales_data', NULL, date, sales,
    'OptimizedTheta', 14, '1d',
    MAP{}
);

Best for: Better accuracy than basic Theta through parameter optimization.

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DynamicTheta

Theta method with time-varying parameters.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period

Example

SELECT * FROM ts_forecast_by(
    'changing_data', NULL, date, value,
    'DynamicTheta', 28, '1d',
    MAP{}
);

Best for: Series with changing patterns over time.

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DynamicOptimizedTheta

Combines dynamic and optimized Theta approaches.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period

Example

SELECT * FROM ts_forecast_by(
    'complex_data', NULL, date, value,
    'DynamicOptimizedTheta', 28, '1d',
    MAP{}
);

Best for: Maximum Theta accuracy with dynamic adaptation.

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Comparison

Model	Speed	Optimization	Best Use Case
Theta	Fast	None	Quick baseline
AutoTheta	Fast	Automatic	General purpose
OptimizedTheta	Fast	Parameters	Better accuracy
DynamicTheta	Medium	Time-varying	Changing patterns
DynamicOptimizedTheta	Medium	Both	Maximum accuracy

When to Use Theta Methods

Scenario	Recommended
Quick forecast needed	Theta
Production system	AutoTheta
Maximum accuracy	DynamicOptimizedTheta
Changing patterns	DynamicTheta
Limited data	Theta
External predictors	ThetaX

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ThetaX

Theta method with exogenous (external) variables. Combines Theta's simplicity with external predictor support.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period

Example

-- Create future exogenous values
CREATE TABLE future_exog AS
SELECT * FROM (VALUES
    ('2024-01-08'::DATE, 22.0),
    ('2024-01-09'::DATE, 20.0),
    ('2024-01-10'::DATE, 21.0)
) AS t(date, temperature);

-- Forecast with exogenous variables
SELECT * FROM ts_forecast_exog_by(
    'sales_data', NULL, date, sales,
    ['temperature'],
    'future_exog', date, ['temperature'],
    'ThetaX', 3,
    MAP{}, '1d'
);

Best for: Short-term forecasts with external drivers, simple models with predictor support.

See Exogenous Variables for detailed usage