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Four-model comparison

Price Prediction Workbench

Compare historical bootstrap, block bootstrap, correlated Monte Carlo, and heavy-tail Student-t projections at the same time. Advance all four synthetic paths together, then back up one complete step when needed.

These are simulated conditional distributions, not literal forecasts or guarantees. Bands describe model dispersion under historical assumptions; they do not establish where price must trade.

Prediction settings

The first ticker is the displayed prediction. Additional symbols are optional covariance context for the multivariate models.

Recommended defaults

XSP daily 63-day horizon, 800 paths, five-day blocks.
XSP intraday Five- or 15-minute data, 52 intervals ahead, 800 paths.
End-of-day projection Choose intraday data and “Until end of trading day.” The horizon contracts to the applicable market close.
Context basket Try XSP, SPY, QQQ, ^VIX. The first ticker remains the displayed output.
Interpretation Model agreement is useful context; disagreement is itself a risk signal.

Advance or restore the model paths

Each repeat is a separate undoable step. All four models advance before the next repeat begins.

0 simulated trading days · 0 undo points
Current observed price 741.32 Market data through 2026-07-27
All-model median 765.88 64.6% finish above anchor
Consensus 5th percentile 665.56 pooled lower band
Consensus 95th percentile 872.81 pooled upper band
Run settings
Projection horizon 63 trading days
Paths 800 per model 3,200 total across four models

All four median projections

This chart isolates the center path from each model so disagreement is easy to see.

Yahoo Finance ^XSP daily; ^XSP: cache/Yahoo Finance
Comparison of all four model median projections

Consensus projection bands

The pooled bands combine paths from all four models rather than treating one model as authoritative.

Data through 2026-07-27
Consensus price projection fan chart

Stepped paths so far

These are the four independently evolving model anchors. Back one step restores all four together.

Historical path of each stepped simulation model
1 of 4

Historical bootstrap

Resamples individual observed return rows. Cross-asset relationships from each sampled row are preserved.

Current anchor 741.32
Historical bootstrap projection with percentile bands
Median terminal767.45
Probability up64.1%
Median move+3.52%
5th percentile665.01
95th percentile874.30
Modeled range-10.3% to +17.9%
2 of 4

Block bootstrap

Resamples consecutive return blocks to preserve short-term volatility clustering and serial structure.

Current anchor 741.32
Block bootstrap projection with percentile bands
Median terminal762.07
Probability up62.1%
Median move+2.80%
5th percentile660.32
95th percentile863.94
Modeled range-10.9% to +16.5%
3 of 4

Correlated Monte Carlo

Draws jointly from the historical mean vector and covariance matrix. With one ticker, this reduces to Gaussian Monte Carlo.

Current anchor 741.32
Correlated Monte Carlo projection with percentile bands
Median terminal769.73
Probability up67.0%
Median move+3.83%
5th percentile669.33
95th percentile876.39
Modeled range-9.7% to +18.2%
4 of 4

Heavy-tail Student-t

Uses a multivariate Student-t process with five degrees of freedom to allow more frequent extreme moves.

Current anchor 741.32
Heavy-tail Student-t projection with percentile bands
Median terminal765.01
Probability up65.1%
Median move+3.20%
5th percentile668.55
95th percentile880.67
Modeled range-9.8% to +18.8%

What “prediction” means here

Each model estimates a conditional distribution from historical returns. The median is not a guaranteed target, and the 5th–95th percentile band is not a confidence interval for the true future. It is the range containing 90% of simulated outcomes under that model and its current settings.