File 03 — The Turkey
The Turkey
Every year the trend holds, the forecast gets more certain. Ask the turkey how that ends.
A market goes up for twenty years. You fit a line to it, and the arithmetic rewards you: every year the trend survives, the error bars close in, and a genuine walk-forward backtest — refit each year, scored on the year it hasn't seen — comes back clean. Then the world changes, and the future walks straight out of the band. Watch the model's confidence peak, and go on climbing for a year after the break, because two strange years cannot outvote twenty calm ones. Turn one dial — how steady the good years were — and the very same collapse is scored at 3 sigma, or at 24. Goldman's CFO called it a 25-sigma week in 2007. He was describing his model, not the market.
A market grows. You fit a line to it — on log paper, so steady growth is straight. Every year the line holds, the fit tightens and the model gets surer. The dotted outline is the same forecast made six years earlier; watch today’s band sit inside it. That is the narrowing, and it runs across the years, not across the page — any honest forecast still fans out toward the future.
what the model believes today — year 19
the trend it has learned
+9% / yr
fitted on 20 straight years of it
its forecast for year 24
±11%
around 832 — a band that narrows every year the trend holds
walk-forward backtest
15/15
years that landed inside the band the model drew before seeing them calibrated
Nothing here is wrong. The line is a good line, the band is an honest band, and the backtest is a real one — refit each year, judged on the year it had not yet seen. Push the years forward.
What the dials are doing. The model is ordinary least squares on the log of the level. Its forecast band has half-width t·σ·√(1 + 1/n + (x₀−x̄)²/Sxx) — so it tightens with every year n of a trend that holds, and tightens faster the smaller the scatter σaround it. That is all “how sure the model is” ever meant: a measurement of how consistent the past has been. Nothing in the formula is a promise about the future, and nothing in the data can be. The break arrives from outside the series — which is why no amount of it, however clean, could have warned you.
Its two siblings shake a different variable each. The Monte Carlo Fan shakes the path around a growth rate you claim to know. The Fog Behind the Number shakes the rate itself. This one leaves both alone and breaks the world instead — the uncertainty no honest error bar contains.
The essay
Twenty Good Yearsread →