Time Series Lab: Decomposition, ETS & ARIMA Forecast
A complete forecasting workbench in the browser. Paste or drop a CSV with a date column (or plain values), and the lab detects the frequency and seasonal period, splits the series into trend, seasonal pattern and remainder with an STL-style loess decomposition, fits the best exponential-smoothing state-space model (ETS: level, damped trend, additive or multiplicative season) and the best seasonal ARIMA by AICc, and forecasts ahead with 80% and custom prediction intervals. Rolling-origin cross-validation then scores every model against naive, seasonal-naive and drift baselines (MAE, RMSE, MAPE, MASE), so the headline forecast is the one that actually predicted best out of sample — not the one that fit best in hindsight.
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Results
Notes
- Decomposition is STL-style: a periodic seasonal component and a loess trend, iterated with bisquare robustness weights so outliers land in the remainder. Strengths Fₜ and Fₛ are Wang–Smith–Hyndman measures: 1 − Var(remainder)/Var(component + remainder).
- ETS variants tried: no / additive / damped trend × no / seasonal component, all with additive errors, fitted by maximising the Gaussian likelihood over smoothing parameters and initial states; the lowest AICc wins.
- ARIMA: seasonal differencing when seasonal strength exceeds 0.64, ordinary differencing until a KPSS test accepts stationarity, then (p,q)≤(3,3) and seasonal (P,Q)≤(1,1) screened by Hannan–Rissanen regressions and the best six refitted by conditional least squares. AICc is only comparable between models with the same differencing.
- MASE scales errors by the in-sample seasonal-naive error: below 1 beats copying last season; above 1 you would have done better with no model.
- A Ljung–Box p-value under 0.05 says the residuals still carry structure the model missed — the intervals are then too narrow.
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