Theta · Pro
Theta
SES plus a drift line — the M3-famous combination (Pro).
What it assumes
SES combined with a drift (Theta-line) — M3-famous.
When to use
Macro / mildly trended series.
When to avoid
Strong seasonal retail without a seasonal wrapper.
Knobs
ŷ = SES + 0.5·h·drift. Pro.
How it works
The classic Theta method combines a smoothed level (SES) with a drift (“theta line”). It did remarkably well on the M3 competition for many mildly trended macro series. Strong retail seasonality without a seasonal wrapper is a known weakness. In WhichForecast it is a Pro family; Free users still see the DNA row, soft-locked.
Sample forecast question
A quarterly indicator drifts up with little calendar shape. What is the Theta forecast for the next four quarters?
Step-by-step on these numbers
| Period | Actual | Fitted |
|---|---|---|
| Y1 Q1 | 14 | 14 |
| Y1 Q2 | 15 | 14 |
| Y1 Q3 | 16 | 14.95 |
| Y1 Q4 | 16 | 15.95 |
| Y2 Q1 | 18 | 16.00 |
| Y2 Q2 | 19 | 17.90 |
| Y2 Q3 | 20 | 18.94 |
| Y2 Q4 | 21 | 19.95 |
| Y3 Q1 | 22 | 20.95 |
| Y3 Q2 | 23 | 21.95 |
| Period | Forecast | 95% interval |
|---|---|---|
| Y3 Q3 | 23.45 | 22.34 – 24.56 |
| Y3 Q4 | 23.95 | 22.38 – 25.52 |
| Y4 Q1 | 24.45 | 22.52 – 26.37 |
| Y4 Q2 | 24.95 | 22.72 – 27.17 |
Parameters the engine found
alpha= 0.950last= 22.947drift= 1
The question
A quarterly indicator drifts up with little calendar shape. What is the Theta forecast for the next four quarters? Sample quarters: Y1 Q1=14, Y1 Q2=15, Y1 Q3=16, Y1 Q4=16, Y2 Q1=18, Y2 Q2=19, Y2 Q3=20, Y2 Q4=21, Y3 Q1=22, Y3 Q2=23 (index).
SES + drift
Classic Theta (M3) combines a SES level with a drift line. SES α = 0.950 gives last level 22.95. Drift = (23 − 14)/9 = 1.
Forecast rule
ŷ_{n+h} = SES_last + 0.5 · h · drift. The ½ is the usual Theta-line weight in this engine. Y3 Q3 = 22.95 + 0.5×1×1 = 23.45; Y3 Q4 = 22.95 + 0.5×2×1 = 23.95; Y4 Q1 = 22.95 + 0.5×3×1 = 24.45; Y4 Q2 = 22.95 + 0.5×4×1 = 24.95.
Interval
Residual σ = 0.567. For h = 1 the 95% band is [22.34, 24.56] around 23.45. The engine labels this a residual-Gaussian heuristic (σ√h), not a simulation interval.
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.”