Baselines · Free
Seasonal naive
Copy last year’s value for the same season.
What it assumes
The value repeats from the same season last year/cycle.
When to use
Stable seasonal pattern, enough history for at least one full cycle.
When to avoid
Changing seasonality, or m unknown / too short a sample.
Knobs
ŷ_{t+h} = y_{t+h−m}. m is the seasonal period.
How it works
Seasonal naive looks back one full cycle: ŷ_{t+h} = y_{t+h−m}. For quarterly data, m = 4 — next Q1 equals last Q1. It is the seasonal counterpart of naive and the second FVA baseline. It needs at least one complete cycle and a stable seasonal shape.
Sample forecast question
Two years of quarterly counts show a repeating seasonal shape. What is the seasonal-naive forecast for the next four quarters?
Step-by-step on these numbers
| Period | Actual | Fitted |
|---|---|---|
| Y1 Q1 | 18 | 18 |
| Y1 Q2 | 29 | 29 |
| Y1 Q3 | 22 | 22 |
| Y1 Q4 | 31 | 31 |
| Y2 Q1 | 19 | 18 |
| Y2 Q2 | 30 | 29 |
| Y2 Q3 | 23 | 22 |
| Y2 Q4 | 32 | 31 |
| Period | Forecast | 95% interval |
|---|---|---|
| Y3 Q1 | 19 | 17.95 – 20.05 |
| Y3 Q2 | 30 | 28.52 – 31.48 |
| Y3 Q3 | 23 | 21.19 – 24.81 |
| Y3 Q4 | 32 | 29.90 – 34.10 |
Parameters the engine found
m= 4lastSeasonMean= 26
The question
Two years of quarterly counts show a repeating seasonal shape. What is the seasonal-naive forecast for the next four quarters? Sample quarters: Y1 Q1=18, Y1 Q2=29, Y1 Q3=22, Y1 Q4=31, Y2 Q1=19, Y2 Q2=30, Y2 Q3=23, Y2 Q4=32 (shipments).
Seasonal period
m = 4. Seasonal naive copies the last complete cycle: ŷ_{t+h} = y_{t+h−m}.
Last cycle
The last 4 observations are Y2 Q1=19, Y2 Q2=30, Y2 Q3=23, Y2 Q4=32. Those values are written forward in order.
Forecast
Y3 Q1: 19; Y3 Q2: 30; Y3 Q3: 23; Y3 Q4: 32.
Interval
Residual σ = 0.535. For h = 1 the 95% band is [17.95, 20.05] around 19. The engine labels this interval native for the method.
Graph of this sample
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.
Educational only. Not investment, weather, or operational advice. In the add-in, rank is rolling-origin MASE — “best supported among candidates on this series.”