TESLTMS (Triple Exponential Smoothing with Linear Trend and Multiplicative Seasonality)

TESLTMS (Triple Exponential Smoothing with Linear Trend and Multiplicative Seasonality) function, we use the hw() function with seasonal = "multiplicative".

This is the preferred model for data where seasonal spikes grow in proportion to the trend.

Example: - A 20% increase every December becomes a larger absolute value each year as the trend increases.

Zero Constraint (Important)

Multiplicative models perform division by seasonal factors.

Rule:

  • If your data contains zeros or negative numbers, this function will crash
  • In such cases, use:
  • TESLTAS (Additive Seasonality Model)

Seasonal Multiplier Concept

  • Additive Model:
    → “Add 50 to the forecast”

  • Multiplicative Model:
    → “Multiply the forecast by 1.15”

Key Idea:

  • Seasonal effects grow as the trend grows
  • Spikes become larger over time

Parameters

  • Alpha (α): Level (base smoothing)
  • Beta (β): Trend (slope smoothing)
  • Gamma (γ): Seasonality (seasonal smoothing)

Key Points

  • Uses Holt-Winters exponential smoothing
  • Best for growing seasonal patterns
  • Seasonal effects are percentage-based
  • Requires strictly positive data
  • Implemented using hw(seasonal = "multiplicative")

When to Use

Use TESLTMS when: - Seasonality increases with trend - Data shows proportional seasonal growth - Example: sales, demand, traffic with growth cycles

When NOT to Use

  • Data contains 0 values
  • Data contains negative values
  • Seasonal pattern is constant (use additive instead)