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Holt linear

Local level plus a linear trend (α and β).

How it works

Holt adds a trend equation to SES. Each period the level and the slope are updated with weights α and β. The h-step forecast is level + h × trend. That line will keep climbing forever, so a trend that is dying should use damped trend, and a seasonal cycle should use Holt–Winters. The engine grid-searches the weights, then ranks on walk-forward MASE.

Sample forecast question

A new item’s monthly units rose from 10 to 23. What is Holt’s linear forecast for the next three months?

Step-by-step on these numbers

1. The question

   A new item’s monthly units rose from 10 to 23. What is Holt’s linear forecast for the next three months? Sample months: Jan=10, Feb=12, Mar=13, Apr=16, May=17, Jun=19, Jul=21, Aug=23 (units).

2. Two states

   Holt tracks a level and a slope. Initialise ℓ_0 = y_1 = 10, b_0 = y_2 − y_1 = 2. One-step fitted value is ℓ + b.

3. Weights

   The engine searches a small (α, β) grid. Winner: α = 0.800, β = 0.100.

4. End states

   After the last observation: level ℓ = 22.95, trend b = 1.83. Forecast ŷ_{n+h} = ℓ + h·b.

5. Forecast

   Sep = 22.95 + 1×1.83 = 24.78; Oct = 22.95 + 2×1.83 = 26.62; Nov = 22.95 + 3×1.83 = 28.45.

6. Interval

   Residual σ = 0.919. For h = 1 the 95% band is [22.98, 26.59] around 24.78. The engine labels this interval native for the method.

Graph of this sample

Related methods: Damped trendDriftHolt–Winters additive

Educational only. Not investment, weather, or operational advice. In the add-in, rank is rolling-origin MASE — “best supported among candidates on this series.”

Use it in the Excel Add-in