πŸ“Š Holt's Linear Trend Method

Created by Dr. Pedram Jahangiry | Enhanced with Claude

Website YouTube Channel GitHub Profile

Interactive Teaching Tool for Understanding Level and Trend Components

🎯 Forecast Equation

Ε·t+h|t = β„“t + hΒ·bt
Forecast = Level + (Horizon Γ— Trend)

πŸ“Š Level Equation

β„“t = Ξ±Β·yt + (1-Ξ±)Β·(β„“t-1 + bt-1)
Smooths between observation and one-step forecast

πŸ“ˆ Trend Equation

bt = Ξ²*Β·(β„“t - β„“t-1) + (1-Ξ²*)Β·bt-1
Smooths the trend estimate

πŸ” Holt vs SES: The Key Difference

SES: Assumes data fluctuates around a constant level β†’ Flat forecasts

Holt: Adds a trend component that captures direction β†’ Sloped forecasts that can follow upward/downward patterns!

0.30
Weight for level updates
0.10
Weight for trend updates (0 = constant trend)
112
Starting level estimate
2.0
Starting trend estimate
500ms

Time Step

0

Current Level

-

Current Trend

-

Training RMSE

-

Test RMSE

-

πŸ“š Parameter Guide: Understanding Alpha (Ξ±) and Beta* (Ξ²*)

🎯 Dual Parameter Control: Level and Trend Components

πŸ“Š Alpha (Ξ±) - Level Smoothing

Controls level responsiveness:

  • Low Ξ± (0.1-0.3): Stable level, slow to adapt
  • High Ξ± (0.7-0.9): Responsive level, quick adaptation

πŸ“ˆ Beta* (Ξ²*) - Trend Smoothing

Controls trend responsiveness:

  • Low Ξ²* (0.1-0.3): Stable trend, resistant to noise
  • High Ξ²* (0.7-0.9): Adaptive trend, follows changes

⚑ High α, Low β*

Level adapts quickly to changes, but trend remains stable. Good for data with level shifts but consistent trend direction.

πŸ”„ Low Ξ±, High Ξ²*

Level changes slowly, but trend adapts quickly. Useful when trend direction changes frequently but level is stable.

🎯 Forecast Impact: Ε·t+h|t = β„“t + hΒ·bt

The forecast combines both components: the current level plus the trend multiplied by the forecast horizon. Longer horizons amplify the trend effect, making Ξ²* increasingly important for long-term forecasts. A stable trend (low Ξ²*) produces consistent long-term forecasts, while an adaptive trend (high Ξ²*) can lead to dramatic fan-out effects.

πŸ”¬ Component Independence

Unlike SES where only Ξ± matters, Holt's method allows independent control over how quickly the model adapts its understanding of "where we are" (level) versus "where we're going" (trend). This dual-parameter approach enables much more nuanced modeling of trending time series patterns.

Experiment with different Ξ± and Ξ²* combinations above to see how they independently control level and trend adaptation!