What is the Time-Series Forecaster multi-solver?

Time-Series Forecaster is a guided workflow that chains 4 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.

Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.

Data & Statistics Pack · Multi-Solver

Time-Series Forecaster

Regress, Fourier, Kalman. This multi-solver chains 4 solvers into a single guided workflow — run each step in order and carry the result forward.

Workflow steps

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Linear Regression

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Linear RegressionLive

least squares & R²

Controls

Presets

True slope

Noise level

Data points

Ordinary least squares finds the line that minimizes the sum of squared vertical residuals (the gray drop-lines). R² measures the fraction of variance the line explains — 1 is perfect, 0 is useless. Add noise or remove points to watch the fit and R² degrade.

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Data Inspector

Fitted slope0.000

Intercept0.000

R²0.000

Correlation r0.000

Governing equation

\overset{y}{^} = 0.00 + 0.00 x, β_{1} = \frac{\sum ( x - x ˉ ) ( y - y ˉ )}{\sum ( x - x ˉ ) ^{2}}, R^{2} = 0.00

Reading this result: R² = 0.00: noise (2) swamps the signal, so least squares can barely tell the slope from flat — adding data points would tighten the estimate.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Fourier

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Fourier Series BuilderLive

synthesize waves from sinusoids

Controls

Add harmonics and watch sine waves sum into a square, sawtooth, or triangle wave — the Fourier series in action.

Presets

Harmonics

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Data Inspector

Wavesquare

Harmonics8

Basissine

Governing equation

f (t) = \frac{a _{0}}{2} + n = 1 \sum 8 (a_{n} cos nω t + b_{n} sin nω t)

Reading this result: Reconstructing the square wave from 8 sine harmonics. More harmonics sharpen the reconstruction and pull it closer to the ideal shape. But at each discontinuity the Gibbs phenomenon leaves a persistent ~9% overshoot spike — adding terms only narrows that ripple, it never removes it, no matter how many harmonics you sum.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Kalman Filter

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Kalman FilterLive

optimal state estimation

Controls

Presets

Measurement noise

Process noise

The Kalman filter fuses a motion model with noisy measurements to track a hidden state optimally. Each step it predicts, then corrects using the Kalman gain — trusting the measurement more when the model is uncertain, and vice versa. It smooths the jittery sensor (gray) into a clean estimate (cyan) that hugs the truth. The math behind GPS, radar, and spacecraft navigation.

▶ Run in Python

Data Inspector

Measurement RMSE0.0

Kalman RMSE0.0

Noise reductionNaN%

Governing equation

\overset{x}{^} \leftarrow \overset{x}{^} + K (z - H \overset{x}{^}), K = \frac{P H ^{T}}{H P H ^{T} + R}, R = 900, Q = 1.00

Reading this result: Measurement noise dwarfs process noise, so the Kalman gain stays small — the filter leans on its motion model and smooths the jitter hard.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Monte Carlo

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Monte Carlo Price SimulationLive

geometric Brownian motion

Controls

Presets

Initial price S₀

Expected return μ

Volatility σ

Horizon (years)

Geometric Brownian motion models a price with constant drift and random volatility — the assumption behind Black-Scholes. Running hundreds of simulated paths reveals the full distribution of outcomes, not just an average. Educational tool, not investment advice.

▶ Run in Python

Data Inspector

Median outcome$0

5th percentile$0

95th percentile$0

Governing equation

S_{t + Δ t} = S_{t} e^{(0.07 - \frac{0. 2 ^{2}}{2}) Δ t + 0.2 Δ t Z}, \tilde{S}_{1} \approx $0

Reading this result: Median outcome is about $0, just under the drift-only $107 — GBM compounds in log-space, so volatility always pulls the typical path below the average.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Frequently asked questions

What is the Time-Series Forecaster multi-solver?: Time-Series Forecaster is a guided workflow that chains 4 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.
Is it free to use?: Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.