WhichForecast

← All methods

Smoothing · Free

Holt–Winters multiplicative

Seasonal swings grow with the level; requires y > 0.

What it assumes

Seasonal swings grow with the level; y > 0.

When to use

Retail-like series with expanding seasonal peaks.

When to avoid

Zeros (undefined / unstable). Spare parts → Croston family.

Knobs

α, β, γ; seasonal indices multiply the level.

How it works

Multiplicative Holt–Winters multiplies the seasonal index by the level, so a 20% summer lift stays 20% as the series grows. Zeros are fatal (division / unstable indices). The candidate policy excludes hw_mul when the series is intermittent. Retail-like positive series with expanding peaks are the intended home.

Sample forecast question

Shop sales are growing and Q4 is always a taller peak. What is the multiplicative Holt–Winters forecast for the next four quarters?

Step-by-step on these numbers

Sample series (sales)
PeriodActualFitted
Y1 Q12021.02
Y1 Q22829.95
Y1 Q32425.81
Y1 Q43638.70
Y2 Q12421.24
Y2 Q23433.24
Y2 Q32929.98
Y2 Q44345.74
Y3 Q13026.10
Y3 Q24240.30
Y3 Q33636.20
Y3 Q45455.62
Forecast
PeriodForecast95% interval
Y4 Q133.5429.30 – 37.78
Y4 Q246.4440.44 – 52.44
Y4 Q340.1332.79 – 47.48
Y4 Q461.3252.83 – 69.80

Parameters the engine found

  • alpha = 0.600
  • beta = 0.050
  • gamma = 0.500
  • level = 42.115
  • trend = 1.355
  • m = 4
  • s0 = 0.772
  • s1 = 1.036
  • s2 = 0.869
  • s3 = 1.290

  1. The question

    Shop sales are growing and Q4 is always a taller peak. What is the multiplicative Holt–Winters forecast for the next four quarters? Sample quarters: Y1 Q1=20, Y1 Q2=28, Y1 Q3=24, Y1 Q4=36, Y2 Q1=24, Y2 Q2=34, Y2 Q3=29, Y2 Q4=43, Y3 Q1=30, Y3 Q2=42, Y3 Q3=36, Y3 Q4=54 (sales).

  2. Seasons

    m = 4, n = 12 (3 complete seasons). Multiplicative HW needs y > 0 (this sample is strictly positive).

  3. Initialisation

    Season averages: S1=27, S2=32.50, S3=40.50. Initial level ℓ = 27, initial trend b = (32.50 − 27)/4 = 1.38. Initial seasonal indices from the first cycle: s_1=0.741, s_2=1.037, s_3=0.889, s_4=1.333.

  4. Smoothing weights

    The engine searches a small (α, β, γ) grid. Winner: α = 0.600, β = 0.050, γ = 0.500.

  5. End states

    ℓ = 42.12, b = 1.36, seasonal vector [0.772, 1.036, 0.869, 1.290].

  6. Forecast

    ŷ_{n+h} = (ℓ + h b) × s_h. Y4 Q1: 43.47 × 0.772 → 33.54; Y4 Q2: 44.83 × 1.036 → 46.44; Y4 Q3: 46.18 × 0.869 → 40.13; Y4 Q4: 47.54 × 1.290 → 61.32.

  7. Interval

    Residual σ = 2.165. For h = 1 the 95% band is [29.30, 37.78] around 33.54. The engine labels this interval native for the method.

Graph of this sample

Y1 Q1 · 20 Y3 Q4 Y4 Q1
Holt–Winters multiplicative on the canned sample: actuals, fitted, and a 4-step forecast. Actual Fitted Forecast
The chart plots the canned table on this page (actuals, in-sample fitted, forecast, 95% interval). Not your Excel series. Free analysis never uploads raw data.

Related methods: Holt–Winters additiveSeasonal naiveCroston

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