Exponential Smoothing

Weighted average methods where recent observations have more influence than older ones.

Model	Description
ETS	Error-Trend-Seasonality state space model
AutoETS	Automatic ETS with component selection
SES	Simple Exponential Smoothing
SESOptimized	SES with optimized smoothing parameter
Holt	Linear trend method
HoltWinters	Trend + seasonality
SeasonalES	Seasonal exponential smoothing
SeasonalESOptimized	SeasonalES with optimized parameters

Showing 8 of 8

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ETS (Error-Trend-Seasonality)

State space model with explicit error, trend, and seasonal components.

Parameters

Parameter	Type	Default	Description
error	VARCHAR	'A'	Error type: A (Additive), M (Multiplicative)
trend	VARCHAR	'A'	Trend type: A, M, N (None)
seasonal	VARCHAR	'A'	Seasonal type: A, M, N
seasonal_period	INTEGER	-	Seasonal period (required if seasonal != 'N')

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'sales_data',
    'date',
    'sales',
    'ETS',
    28,
    MAP{'trend': 'A', 'seasonal': 'A', 'seasonal_period': '7'}
);

Best for: Trending + seasonal data, smooth patterns.

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AutoETS

Automatic ETS with component selection using information criteria.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period (auto-detected if not specified)
confidence_level	DOUBLE	0.90	Prediction interval width

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'sales_data',
    'date',
    'sales',
    'AutoETS',
    28,
    MAP{'seasonal_period': '7', 'confidence_level': '0.95'}
);

Best for: Most common use case, default choice for trend + seasonality.

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SES (Simple Exponential Smoothing)

Weighted average of past observations with exponentially decreasing weights.

Parameters

Parameter	Type	Default	Description
alpha	DOUBLE	auto	Smoothing parameter (0-1)

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'stable_data',
    'date',
    'value',
    'SES',
    14,
    MAP{}
);

Best for: No trend, no seasonality, stationary data.

---

SESOptimized

SES with automatically optimized smoothing parameter.

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'stable_data',
    'date',
    'value',
    'SESOptimized',
    14,
    MAP{}
);

Best for: Stationary data with automatic parameter tuning.

---

Holt (Linear Trend)

Extends SES to capture linear trends.

Parameters

Parameter	Type	Default	Description
alpha	DOUBLE	auto	Level smoothing
beta	DOUBLE	auto	Trend smoothing

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'trending_data',
    'date',
    'value',
    'Holt',
    28,
    MAP{}
);

Best for: Linear trending data without seasonality.

---

HoltWinters

Extends Holt to include seasonality (additive or multiplicative).

Parameters

Parameter	Type	Default	Description
seasonal	VARCHAR	'additive'	'additive' or 'multiplicative'
seasonal_period	INTEGER	-	Seasonal period (required)

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'retail_sales',
    'date',
    'sales',
    'HoltWinters',
    52,
    MAP{'seasonal': 'multiplicative', 'seasonal_period': '7'}
);

Best for: Clear trend + seasonality patterns.

---

SeasonalES

Seasonal exponential smoothing without trend component.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	-	Seasonal period (required)

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'seasonal_data',
    'date',
    'value',
    'SeasonalES',
    28,
    MAP{'seasonal_period': '7'}
);

Best for: Seasonal patterns without trend.

---

SeasonalESOptimized

SeasonalES with optimized parameters.

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'seasonal_data',
    'date',
    'value',
    'SeasonalESOptimized',
    28,
    MAP{'seasonal_period': '7'}
);

Best for: Seasonal patterns with automatic parameter tuning.

---

Comparison

Model	Trend	Seasonality	Parameters
SES	No	No	alpha
SESOptimized	No	No	auto
Holt	Yes	No	alpha, beta
HoltWinters	Yes	Yes	alpha, beta, gamma
SeasonalES	No	Yes	alpha, gamma
SeasonalESOptimized	No	Yes	auto
ETS	Configurable	Configurable	Full state space
AutoETS	Auto	Auto	Automatic selection

When to Use AutoETS

AutoETS is recommended as the default choice for most forecasting tasks:

• Automatically selects error, trend, and seasonal components
• Handles both additive and multiplicative patterns
• Produces prediction intervals
• Fast and reliable