Mathematics · advanced
Stationarity & Autocorrelation
When series statistics are stable; memory in lags; noise vs signal.
Mental model
Stationarity: distribution doesn't drift. Autocorrelation: how today relates to yesterday. Random-walk returns have ~0 autocorr; momentum must prove structure exists.
How to study Stationarity & Autocorrelation
Begin by restating the mental model in your own words, then connect it to a concrete system you have built or operated. Name the mechanism, the constraint it addresses, and the trade-off it introduces. Use StatQuest — Stationarity, Forecasting: Principles and Practice, 3rd ed. (Hyndman & Athanasopoulos), FPP3 — 9.1 Stationarity and differencing to check details, but close the source before writing your explanation. Retrieval is the learning step; rereading is only preparation.
Next, compare Stationarity & Autocorrelation with Random Walks & Markov Chains, Momentum Backtest Discipline. Ask what changes in correctness, latency, resource use, operability, and failure recovery. Complete Interpret an ACF plot and preserve the command, input, output, and one failed attempt as evidence. Finish by explaining the idea without jargon to someone who has not studied the track.
Proof of understanding
- Explain the mechanism from first principles and identify the state it reads or changes.
- Give one situation where the concept is the right choice and one where it is not.
- Predict a realistic failure mode before running the drill, then compare the prediction with evidence.
- Connect the result to a roadmap or build artifact instead of treating the concept as isolated trivia.
Where it matters
ARIMA intuition, pairs trading skepticism.
Common mistakes
- Tests on non-stationary levels
- Trend mistaken for momentum
- Ignoring regime shifts
Learn from primary sources
Practice and explain it back
Interpret an ACF plot
Daily returns show ACF lag-1 ≈ 0.02, all within confidence band. Prices show ACF lag-1 ≈ 0.98. Interpret each — which series is closer to a random walk in returns?
Expected evidence: Return ACF ≈0 → little linear memory (efficient-market-ish). Price ACF high → non-stationary levels; difference of prices (returns) matters.
Open the interactive drill →Review prompts
- Why does stationarity matter for inference?
Build evidence
Use a roadmap capstone to turn this concept into working evidence.