A research note that cannot reproduce a one-step forecast from a known DGP will not survive a code review. This lab builds a small, seeded Python pipeline: simulate an AR(1) (and optionally a GARCH(1,1) innovation scale), estimate the conditional mean by OLS, inspect a residual autocorrelation check, and produce one forecast — with expected output in comments. It operationalises ARMA and touches the variance object from ARCH and GARCH without requiring specialised GARCH packages.
Learning objectives. By the end of this note you should be able to:
- simulate a seeded AR(1) path and estimate by OLS on the demeaned series;
- compute lag-1 residual autocorrelation as a residual check;
- form the one-step forecast ;
- optionally overlay GARCH(1,1)-style heteroscedastic innovations and observe residual squares clustering.
In this lesson
- Lab design
- Python lab
- Optional: GARCH innovations, same mean estimator
- Method checklist
Before you start
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