DESAS (Double Exponential Smoothing with Additive Seasonality)

DESAS (Double Exponential Smoothing with Additive Seasonality) is a time series forecasting technique used when data shows both a trend and additive seasonality.

It extends Holt’s Linear Trend Method by adding a seasonal component, allowing forecasts to follow a trend + repeating seasonal pattern.

Model Type

• Exponential Smoothing Model
• ETS Family Model:
• ETS(A, A, A)
  • A → Additive Error
  • A → Additive Trend
  • A → Additive Seasonality

Key Idea

DESAS produces forecasts that: - Follow a linear trend - Repeat a seasonal pattern - Adjust seasonality dynamically over time

Final output = Trend + Seasonality (additive combination)

Parameters

DESAS uses three smoothing parameters:

α (Alpha) — Level

• Controls smoothing of the baseline level
• Higher α → reacts quickly to recent data
• Lower α → smoother level changes

β (Beta) — Trend

• Controls how quickly trend changes
• Higher β → fast-changing trend
• Lower β → stable trend

γ (Gamma) — Seasonality

• Controls seasonal adjustment strength
• Higher γ → seasonal pattern adapts quickly
• Lower γ → stable repeating seasonality

Seasonal Frequency Requirement

Seasonality must be explicitly defined using frequency (m):

Data Type	Frequency
Monthly	12
Weekly	7
Daily with weekly cycle	7
Quarterly	4

Without frequency, seasonal cycles cannot be modeled correctly.

Implementation (R)

Using Holt-Winters (hw())

library(forecast)

model <- hw(data, seasonal = "additive")
forecast_values <- forecast(model)