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Decomposition · Free

Decompose + seasonal naive

Pull off a seasonal pattern, then naive the remainder.

How it works

Classical seasonal means (centred) estimate a repeating shape. Subtract that shape, take the last deseasonalized level, then add the seasonal indices back for future periods. It is a teaching decomposition more than a state-of-the-art engine. Evolving or multiplicative seasonality will look wrong — Holt–Winters or SARIMA may fit better, and the backtest decides.

Sample forecast question

Classroom series: subtract a quarterly seasonal pattern, hold the leftover level, then put the pattern back. What are the next four quarterly forecasts?

Step-by-step on these numbers

1. The question

   Classroom series: subtract a quarterly seasonal pattern, hold the leftover level, then put the pattern back. What are the next four quarterly forecasts? Sample quarters: Y1 Q1=12, Y1 Q2=18, Y1 Q3=16, Y1 Q4=9, Y2 Q1=13, Y2 Q2=19, Y2 Q3=17, Y2 Q4=10, Y3 Q1=14, Y3 Q2=20, Y3 Q3=18, Y3 Q4=11 (°C).

2. Seasonal means

   Overall mean μ = 14.750. For each season, average (y − μ), then centre the indices so they sum to ~0. Indices: [-1.750, 4.250, 2.250, -4.750].

3. Deseasonalize

   y*_t = y_t − s_{t mod m}. The last deseasonalized level is 15.75. The forecast adds the matching seasonal index back onto that level (seasonal naive on the remainder).

4. Forecast

   Y4 Q1 = 15.75 + -1.750 = 14; Y4 Q2 = 15.75 + 4.250 = 20; Y4 Q3 = 15.75 + 2.250 = 18; Y4 Q4 = 15.75 + -4.750 = 11.

5. Interval

   Residual σ = 0.492. For h = 1 the 95% band is [13.03, 14.97] around 14. The engine labels this a residual-Gaussian heuristic (σ√h), not a simulation interval.

Graph of this sample

Related methods: Seasonal naiveHolt–Winters additiveTime-series linear model

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