What is the AR(2) model on the VIX forecast?

The AR(2) chip on the VIX forecast is a second-order autoregression on log(VIX): it predicts the next reading from the last two days instead of one. That extra lag lets the forecast carry short-term momentum — a fresh volatility spike keeps rising for a few days before the pull back toward equilibrium takes over.

Why the momentum term fits VIX

The plain log-OU baseline reverts smoothly and immediately toward its long-run mean. But volatility doesn't behave that way: a VIX spike tends to persist for several sessions — a shock on Monday is usually still elevated on Wednesday — before it decays back to calm. AR(2) captures that stickiness by remembering the last two moves, so a jump has measured follow-through built in rather than snapping straight back. Like every VIX model here it works in log-space, so its paths stay positive and keep VIX's right-skewed spike-and-decay shape.

Where it sits — and how to judge it

AR(2) is a small, disciplined step up from the log-OU baseline: two lags instead of one, no exotic machinery. Whether that step is worth it on current data is a question you can answer directly — the "Model performance" table under the VIX forecast re-runs the walk-forward backtest and shows AR(2)'s coverage, MAPE, RMSE, Brier and directional hit-rate right beside the log-OU baseline and the Market Conditions model.

Frequently asked questions

How is the VIX AR(2) different from the OU baseline?

The log-OU baseline reverts smoothly from one day's reading. AR(2) looks at the last two days of log(VIX), so it can carry short-term momentum — a fresh spike keeps rising briefly before the pull toward equilibrium dominates.

Why does a momentum term suit volatility?

Because VIX spikes tend to persist for several sessions rather than snapping back instantly — a shock on Monday is usually still elevated on Wednesday. The second lag lets the forecast reflect that follow-through.

Is AR(2) better than the OU baseline?

That depends on current data. The 'Model performance' table under the VIX forecast shows AR(2) and log-OU side by side on coverage, MAPE, RMSE, Brier and hit-rate so you can compare them directly.

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Educational research only — not investment advice.