WhichForecast

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ARIMA · Free

SARIMA

ARIMA plus a seasonal-difference proxy; needs n ≥ 3m.

What it assumes

ARIMA plus a seasonal-difference proxy blended with seasonal naive.

When to use

Seasonal series with leftover ARMA errors.

When to avoid

n < 3m.

Knobs

Nonseasonal (p,d,q) + seasonal period m.

How it works

SARIMA is offered only when the seasonal period m is known and the series is long enough (n ≥ 3m). The Free implementation is a conservative blend: a small nonseasonal ARIMA grid plus a seasonal-difference / seasonal-naive proxy — not a giant seasonal (P,D,Q) search. If n is short, the policy excludes it and explains why.

Sample forecast question

Four years of quarterly bookings (n = 16, m = 4). What is the SARIMA-lite forecast for the next four quarters?

Step-by-step on these numbers

Sample series (bookings)
PeriodActualFitted
Y1 Q12020
Y1 Q22820
Y1 Q32423.20
Y1 Q43626.40
Y2 Q12228.80
Y2 Q23030.40
Y2 Q32525.20
Y2 Q43828
Y3 Q12330.20
Y3 Q23232
Y3 Q32726.60
Y3 Q44030
Y4 Q12532.20
Y4 Q23434
Y4 Q32828.60
Y4 Q44231.60
Forecast
PeriodForecast95% interval
Y5 Q129.3017.21 – 41.39
Y5 Q236.3219.22 – 53.42
Y5 Q331.8110.87 – 52.75
Y5 Q439.7215.54 – 63.89

Parameters the engine found

  • p = 1
  • d = 1
  • q = 0
  • P = 0
  • D = 1
  • Q = 0
  • m = 4
  • last = 42
  • aicc = 63.900
  • phi1 = -0.600

  1. The question

    Four years of quarterly bookings (n = 16, m = 4). What is the SARIMA-lite forecast for the next four quarters? Sample quarters: Y1 Q1=20, Y1 Q2=28, Y1 Q3=24, Y1 Q4=36, Y2 Q1=22, Y2 Q2=30, Y2 Q3=25, Y2 Q4=38, Y3 Q1=23, Y3 Q2=32, Y3 Q3=27, Y3 Q4=40, Y4 Q1=25, Y4 Q2=34, Y4 Q3=28, Y4 Q4=42 (bookings).

  2. Bounded search

    SARIMA is offered because m = 4 and n = 16 ≥ 3m. The Free engine searches a small nonseasonal (p,d,q ≤ 2) grid plus a seasonal-difference / seasonal-naive blend — not a giant (P,D,Q) search.

  3. Selected model

    ARIMA(1,1,0) with seasonal period m = 4 and seasonal-difference proxy D = 1. Coefficients: φ1 = -0.600. AICc = 63.90.

  4. Forecast

    Iterate the ARMA on the differenced scale, then invert differences and blend 50/50 with seasonal naive. Y5 Q1: 29.30; Y5 Q2: 36.32; Y5 Q3: 31.81; Y5 Q4: 39.72.

  5. Interval

    Residual σ = 6.168. For h = 1 the 95% band is [17.21, 41.39] around 29.30. The engine labels this a residual-Gaussian heuristic (σ√h), not a simulation interval.

Graph of this sample

Y1 Q1 · 20 Y4 Q4 Y5 Q1
SARIMA 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: ARIMAHolt–Winters additiveSeasonal naive

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