This time-series sandbox was generated by Claude (Anthropic) for the STAT 101 course materials. Every number on it is computed in your browser and recomputed on every knob change: the whole moving-average trend, the seasonal component, the residual, the autocorrelation and partial-autocorrelation at every lag, the ±1.96/√N significance bands, the Yule–Walker AR coefficients and the multi-step forecast. Nothing on this page is sketched.
The additive decomposition yₜ = Tₜ + Sₜ + Rₜ reconstructs the series to machine precision, because the residual is defined as yₜ − Tₜ − Sₜ at every point — it is not an approximation. For an AR(1) series the Yule–Walker estimate φ̂ is exactly the lag‑1 autocorrelation.
Classical decomposition, the ACF/PACF and the Yule–Walker equations are standard time-series methods (see e.g. Box & Jenkins; Brockwell & Davis). The trend slope, seasonal amplitude, period, noise level, seed, AR order and horizon are illustrative inputs you set; the arithmetic done on them is exact. Seeded generator: mulberry32 (public domain). No number on this page came from a real dataset — the series is a simulation whose components are chosen and whose draws are reproducible from the seed.
Course demo — reached from the Labs & Demos hub; the page itself is English‑only for now. Built for STAT-101 Module 10. Build a series from a trend, a seasonal wave and noise, then take it apart three ways: a decomposition that splits it back into those pieces, the ACF and PACF that reveal the seasonal period as a spike, and an AR(p) forecast fit by Yule–Walker. Turn the knobs and watch every piece recompute.