Multi-Seasonal Models

Models designed for complex seasonality patterns (e.g., hourly data with daily + weekly cycles).

Model	Description
TBATS	Trigonometric seasonality, Box-Cox, ARMA errors
AutoTBATS	Automatic TBATS with parameter selection
MSTL	Multiple Seasonal-Trend decomposition using Loess
AutoMSTL	Automatic MSTL with period detection
MFLES	Median-based Feature-Logic Expert System
AutoMFLES	Automatic MFLES configuration
MFLESX	MFLES with exogenous variables

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TBATS

Trigonometric seasonality, Box-Cox transformation, ARMA errors, Trend, and Seasonal components.

Parameters

Parameter	Type	Required	Description
seasonal_periods	INTEGER[]	Yes	Multiple seasonal periods (e.g., [24, 168] for hourly data)

Example

-- Hourly data with daily (24) and weekly (168) seasonality
SELECT * FROM anofox_fcst_ts_forecast(
    'hourly_energy',
    'timestamp',
    'consumption',
    'TBATS',
    336,
    MAP{'seasonal_periods': '[24, 168]'}
);

Best for: Multiple seasonal patterns, high-frequency data.

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AutoTBATS

Automatic TBATS with parameter selection.

Parameters

Parameter	Type	Default	Description
seasonal_periods	INTEGER[]	auto	Multiple seasonal periods

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'complex_data',
    'timestamp',
    'value',
    'AutoTBATS',
    336,
    MAP{}
);

Best for: Multiple seasonality with automatic configuration.

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MSTL

Multiple Seasonal-Trend decomposition using Loess. Decomposes series into trend + multiple seasonal components + remainder.

Parameters

Parameter	Type	Required	Description
seasonal_periods	INTEGER[]	Yes	Multiple seasonal periods

Example

-- Daily data with weekly (7) and yearly (365) seasonality
SELECT * FROM anofox_fcst_ts_forecast(
    'daily_sales',
    'date',
    'sales',
    'MSTL',
    90,
    MAP{'seasonal_periods': '[7, 365]'}
);

Best for: Very complex seasonality, decomposition-based forecasting.

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AutoMSTL

Automatic MSTL with period detection.

Parameters

Parameter	Type	Default	Description
seasonal_periods	INTEGER[]	auto	Multiple seasonal periods

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'hourly_data',
    'timestamp',
    'value',
    'AutoMSTL',
    168,
    MAP{}
);

Best for: Complex seasonality with automatic period detection.

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MFLES

Median-based Feature-Logic Expert System. Robust to outliers and noise.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Primary seasonal period

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'noisy_retail',
    'date',
    'sales',
    'MFLES',
    28,
    MAP{'seasonal_period': '7'}
);

Best for: Noisy data, outliers, real-world messy time series.

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AutoMFLES

Automatic MFLES configuration.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'noisy_data',
    'date',
    'value',
    'AutoMFLES',
    28,
    MAP{}
);

Best for: Noisy data with automatic robust forecasting.

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Comparison

Model	Outlier Robust	Speed	Seasonality Handling
TBATS	No	Slow	Trigonometric
AutoTBATS	No	Slow	Auto trigonometric
MSTL	Moderate	Slow	Loess decomposition
AutoMSTL	Moderate	Slow	Auto decomposition
MFLES	Yes	Medium	Median-based
AutoMFLES	Yes	Medium	Auto median-based

When to Use Multi-Seasonal Models

Data Pattern	Recommended Model
Hourly + daily + weekly	AutoTBATS or AutoMSTL
Daily + weekly + yearly	AutoMSTL
Noisy with multiple patterns	AutoMFLES
High-frequency (sub-hourly)	AutoTBATS
Need decomposition output	MSTL

Common Seasonal Periods

Frequency	Common Periods
Hourly	24 (daily), 168 (weekly), 8760 (yearly)
Daily	7 (weekly), 30/31 (monthly), 365 (yearly)
Weekly	52 (yearly)
Monthly	12 (yearly)

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MFLESX

MFLES with exogenous (external) variables. Combines MFLES's robustness to outliers with external predictor support.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Primary seasonal period

Example

-- Create future exogenous values
CREATE TABLE future_exog AS
SELECT * FROM (VALUES
    ('2024-01-08'::DATE, 22.0, 1),
    ('2024-01-09'::DATE, 20.0, 0),
    ('2024-01-10'::DATE, 21.0, 1)
) AS t(date, temperature, promotion);

-- Forecast noisy retail data with exogenous variables
SELECT * FROM ts_forecast_exog(
    'noisy_retail', date, sales,
    'temperature,promotion',
    'future_exog',
    'MFLESX', 3, MAP{}
);

Best for: Noisy data with external drivers, real-world messy time series with predictors.

See Exogenous Variables for detailed usage