Stationarity
Can a market's recent statistical behaviour be trusted to hold, or does the series change its own rules over time?
In plain words
A series is stationary when its basic statistical properties — its average level, the size of its swings, and how today relates to yesterday — stay roughly the same across time. When those properties drift or shift, the series is non-stationary, and a pattern measured in one period may not describe the next.
Why it matters
Nearly every forecast, risk model and sizing rule assumes the recent past is a fair guide to the near future. If a market's volatility regime, trend or correlation structure is shifting, those calibrations quietly stop applying, often just when they matter most.
In a real week: BTC, week of 30 September 2019
In the week of 30 September 2019, BTC returned -2.35% with realised volatility of 52.0% annualised, while the prior four weeks returned 6.76%, -0.76%, -2.66% and -19.79%. Those prior weeks swung between a 6.76% gain and a 19.79% loss, and three of the four were down. Average 8-hour funding was -0.003%, with a peak of 0.01% and a low of -0.0525%. This week's return sat at the 33.0 percentile against 85 weeks of history.
A common mistake
Assuming a market is stationary because a model fitted well on past data. Fit quality says nothing about whether the underlying mean, variance or correlation structure will persist.