Exponential Smoothing

AnoFox provides 8 exponential smoothing models ranging from Simple Exponential Smoothing (SES) with a single parameter to AutoETS with automatic component selection across all error, trend, and seasonal combinations. AutoETS is the recommended default for most forecasting tasks -- it selects the optimal ETS configuration using information criteria and produces prediction intervals without manual tuning.

Exponential smoothing is a family of forecasting methods that assign exponentially decreasing weights to older observations, so recent data points have more influence on the forecast than distant ones. The state space formulation classifies models by their Error (A/M), Trend (N/A/M), and Seasonal (N/A/M) components.

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

---

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 ts_forecast_by(
    'sales_data', NULL, date, sales,
    'ETS', 28, '1d',
    MAP{'trend': 'A', 'seasonal': 'A', 'seasonal_period': '7'}
);

Best for: Trending + seasonal data, smooth patterns.

---

AutoETS

Automatic ETS with component selection using information criteria.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	-	Seasonal period (detect with ts_detect_periods_by first)
confidence_level	DOUBLE	0.90	Prediction interval width

Example

SELECT * FROM ts_forecast_by(
    'sales_data', NULL, date, sales,
    'AutoETS', 28, '1d',
    MAP{'seasonal_period': '7', 'confidence_level': '0.95'}
);

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

---

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 ts_forecast_by(
    'stable_data', NULL, date, value,
    'SES', 14, '1d',
    MAP{}
);

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

---

SESOptimized

SES with automatically optimized smoothing parameter.

Example

SELECT * FROM ts_forecast_by(
    'stable_data', NULL, date, value,
    'SESOptimized', 14, '1d',
    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 ts_forecast_by(
    'trending_data', NULL, date, value,
    'Holt', 28, '1d',
    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 ts_forecast_by(
    'retail_sales', NULL, date, sales,
    'HoltWinters', 52, '1d',
    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 ts_forecast_by(
    'seasonal_data', NULL, date, value,
    'SeasonalES', 28, '1d',
    MAP{'seasonal_period': '7'}
);

Best for: Seasonal patterns without trend.

---

SeasonalESOptimized

SeasonalES with optimized parameters.

Example

SELECT * FROM ts_forecast_by(
    'seasonal_data', NULL, date, value,
    'SeasonalESOptimized', 28, '1d',
    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

The 8 exponential smoothing models form a hierarchy of increasing complexity: SES handles stationary data with 1 parameter, Holt adds trend with 2 parameters, HoltWinters adds seasonality with 3 parameters, and ETS provides the full configurable state space. AutoETS automates the selection process, testing all valid component combinations and choosing the best fit via information criteria. For production pipelines processing thousands of series, AutoETS eliminates manual model selection entirely.

---

Frequently Asked Questions

What is the difference between additive and multiplicative seasonality?

Additive seasonality means the seasonal effect is a constant amount added to the trend (e.g., sales always increase by 500 units in December). Multiplicative seasonality means the seasonal effect scales proportionally with the level (e.g., sales increase by 20% in December). Use multiplicative when the seasonal amplitude grows as the series level increases. AutoETS selects the appropriate type automatically.

Why would I use ETS with manual components instead of AutoETS?

Use manual ETS when you have domain knowledge about your data's structure. For example, if you know your demand has multiplicative seasonality but no trend, specifying ETS(A,N,M) directly avoids searching over unnecessary configurations. This can also be faster for large-scale batch forecasting where the model structure is already known.

How does AutoETS select the best model?

AutoETS fits all valid combinations of Error (A/M), Trend (N/A/M), and Seasonal (N/A/M) components and selects the model with the lowest AIC (Akaike Information Criterion). This balances goodness-of-fit against model complexity, automatically guarding against overfitting. The search typically evaluates 15-30 candidate models depending on the data characteristics.

Can SES or Holt handle seasonal data?

No. SES and Holt do not model seasonality. SES handles only stationary (level-only) data, and Holt handles level + trend. For seasonal data, use HoltWinters (trend + seasonality), SeasonalES (seasonality without trend), or AutoETS (automatic selection). The comparison table above shows which component each model supports.

---