ARIMA
ARIMA is the model professionals reach for when a series has a trend and momentum. The scary name is just three simple jobs stitched together. Take them one letter at a time and it turns into the smartest tool in the statistical toolbox.
Three letters, three jobs
- AR says the next value depends on the values just before it, like momentum carrying forward.
- I (integrated) is the clever trick: instead of the prices, you model the changes from day to day. That removes the trend and leaves a flat, predictable series.
- MA here means "moving average of the recent forecast errors," a self-correction so the model learns from its own recent misses.
A series is stationary when it wanders around a fixed level instead of drifting up or down. Models predict stationary series far better, so the "I" step exists purely to make the data stationary before forecasting.
Step 1: difference the data
Press the toggle. In Prices mode you see NCB drifting upward, hard to model. In Daily changes mode you see the same data after differencing: it hovers around zero. That flat cloud is what ARIMA actually forecasts.
The momentum dial is the AR part. At ฯ = 0 the model expects no carry-over (tomorrow's change is zero, so tomorrow โ today, a random walk). Turn ฯ up and recent moves carry forward. Turn it negative and moves tend to reverse (what went up bounces back down).
What it is great at, and where it slips
Series with clear trend and momentum, especially things measured over regular time steps. It is a workhorse for sales, demand, and economic forecasting.
Patterns are wild or driven by outside shocks. On near-random daily stock moves, its edge over a moving average is often tiny.
Your bill often has a real trend (summer heat pushing it up). ARIMA-style thinking, model the change from month to month, then add it back, is exactly how you turn "it keeps rising" into an actual number. You will try this in the bonus light-bill challenge.
- ARIMA = Auto-Regressive (momentum) + Integrated (differencing) + Moving Average (error correction).
- The I step differences a trending series into flat, stationary daily changes.
- The AR dial ฯ sets how much recent momentum carries into the forecast.
Next: hand the computer many clues at once and let machine learning take over.