Forecast tomorrow

What it is

A forecast is a best guess about numbers we haven’t seen yet. Once you’ve found the pattern in the past — the slow trend and the repeating season — you forecast by simply extending it: keep the trend going and repeat the season into the future. But the world is noisy and the pattern isn’t perfect, so a good forecast also says how unsure it is, with a range that grows the further ahead you look.

Go deeper: the single forecast line is just trend + season projected forward. The shaded cone around it is the uncertainty. It starts narrow — next month is almost like this month — and fans wider with each step, because small errors in the trend, in the season, and plain bad luck stack up over time. The width grows roughly like the square root of how far out you go: quickly at first, then more slowly. The real future stays inside the cone, but tends to ride its wide far edge, not the confident tip.

Why care

Forecasts run our world — weather, store inventory, traffic, budgets, climate. The single most important habit is to never trust a forecast number without its range. “Tomorrow: 22°” is useful; “this day next year: 22°” is almost meaningless without admitting it could be far off. A model that hands you a confident single number for a distant future is hiding how little it really knows.

The idea, intuitively

Stand at “now” and look forward. The dashed line is your best guess, following the same up-and-down shape the past taught you. Around it, draw a cone: tight where you’re confident, flaring out where you’re guessing. Slide how far ahead you want to predict and watch the cone open up. Then peek at what actually happened — it lands inside, but rarely right on the line.

Peek at the data first

The history is two years of monthly temperature — the same kind of trend-plus- season series you decomposed earlier. We only ever measure the past; everything past “now” is a forecast. This is the summary Spectra’s describe_data would show before you model it.

Try it

Slide how far ahead to push the dashed forecast and its shaded cone into the future — watch the cone fan wider the further you go. Tick reveal what actually happened to drop the true values onto the chart: they stay inside the cone, but hug its wide outer edge as the horizon grows, never the confident centre.

Where it shows up

• Weather. A 1-day forecast is sharp; a 10-day forecast comes with a wide range of possibilities — that’s the cone in action.
• Business & supply. Stores forecast demand with ranges so they can plan for the best and worst likely cases, not just one guess.
• Climate & planning. Long-range projections are always given as ranges, because uncertainty piles up the further out the forecast reaches.

Where it came from

Modern forecasting grew from weather prediction: in 1922 Lewis Fry Richardson imagined solving the atmosphere with arithmetic, an idea realised once computers arrived in the 1950s. Statisticians George Box and Gwilym Jenkins formalised time-series forecasting in 1970 (the ARIMA methods), and a key part of every modern forecast is the prediction interval — the cone that says how far the truth might stray.

Try it in code

In the Studio, load a time series and plot the history — the trend and season you see are exactly what a forecast extends forward:

data = load "weather_town"
describe_data data

plot_data data, x: "day", y: "temperature"

Open it in the Studio ▶

Check your understanding

• How do you turn a past pattern into a forecast of the future?
• Why does the confidence cone get wider the further ahead you predict?
• Why is a single forecast number for a distant date misleading on its own?