Volatility · Pro
GARCH(1,1)
Variance clustering on returns — not a price oracle. Educational, not advice.
What it assumes
Returns are mean-stationary; variance clusters (ω, α, β). Not a crystal ball for prices.
When to use
Financial / FX returns for interval width.
When to avoid
Raw price levels (use returns workflow). Tiny samples.
Knobs
σ²_t = ω + α r²_{t−1} + β σ²_{t−1}. Mean forecast is μ. Pro.
How it works
GARCH(1,1) models how volatility clusters: σ²_t = ω + α r²_{t−1} + β σ²_{t−1}. The mean forecast is usually a small μ; the useful output is the changing interval width. WhichForecast applies this on a returns workflow, never as “the stock will close at …”. Raw price levels are the wrong input. Tiny samples cannot identify (ω, α, β). This is Pro, and the UI must stay educational.
Sample forecast question
Given these 20 weekly percentage changes, what is next week’s mean-return forecast and how wide is the 95% band? Educational only — not investment advice.
Educational time-series laboratory. Not investment advice. GARCH describes volatility clustering, not a price target.
Step-by-step on these numbers
| Period | Actual | Fitted |
|---|---|---|
| W1 | 0.40 | 0.06 |
| W2 | -0.20 | 0.06 |
| W3 | 0.10 | 0.06 |
| W4 | 0.80 | 0.06 |
| W5 | -1.10 | 0.06 |
| W6 | 0.30 | 0.06 |
| W7 | 0.20 | 0.06 |
| W8 | -0.40 | 0.06 |
| W9 | 1.60 | 0.06 |
| W10 | -0.90 | 0.06 |
| W11 | 0.20 | 0.06 |
| W12 | 0.10 | 0.06 |
| W13 | -0.30 | 0.06 |
| W14 | 0.50 | 0.06 |
| W15 | -0.20 | 0.06 |
| W16 | 0 | 0.06 |
| W17 | 1.20 | 0.06 |
| W18 | -1.40 | 0.06 |
| W19 | 0.30 | 0.06 |
| W20 | -0.10 | 0.06 |
| Period | Forecast | 95% interval |
|---|---|---|
| W21 | 0.06 | -1.31 – 1.42 |
| W22 | 0.06 | -1.31 – 1.42 |
| W23 | 0.06 | -1.31 – 1.42 |
| W24 | 0.06 | -1.31 – 1.42 |
Parameters the engine found
mu= 0.055omega= 0.086alpha= 0.020beta= 0.800lastVar= 0.496lastR= -0.155
The question
Given these 20 weekly percentage changes, what is next week’s mean-return forecast and how wide is the 95% band? Educational only — not investment advice. Sample weeks: W1=0.40, W2=-0.20, W3=0.10, W4=0.80, W5=-1.10, W6=0.30, W7=0.20, W8=-0.40, W9=1.60, W10=-0.90, W11=0.20, W12=0.10, W13=-0.30, W14=0.50, W15=-0.20, W16=0, W17=1.20, W18=-1.40, W19=0.30, W20=-0.10 (% return).
Mean vs variance
GARCH(1,1) is for returns, not price levels. The mean forecast is μ = 0.055 (near zero). The useful output is the changing interval width. This page is educational — not a trading signal.
Variance recurrence
σ²_t = ω + α r²_{t−1} + β σ²_{t−1}. Grid on this sample: ω = 0.0863, α = 0.020, β = 0.800. Last residual r_n = y_n − μ = -0.155; last variance σ²_n = 0.4963.
One-step band
Next variance uses the last shock: σ²_{n+1} = ω + α r_n² + β σ²_n. Point forecasts stay at μ. W21: 0.06; W22: 0.06; W23: 0.06; W24: 0.06. 95% band for the first week: [-1.31, 1.42].
Later horizons
Variance mean-reverts via ω + (α+β)σ². Residual σ = 0.710. For h = 1 the 95% band is [-1.31, 1.42] around 0.06. 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.”