Stationarity, White Noise, and the ACF/PACF

A mean-reversion signal is only useful if its behaviour today is comparable with its behaviour next month. Stationarity makes that comparison legitimate: it says that the distributional features used to estimate an ARMA model do not drift merely because the calendar advances. This note defines the stationarity baseline, then turns the ACF and PACF into cautious identification evidence for a return, yield, or spread.

• distinguish strict from covariance stationarity;
• define white noise and autocorrelation;
• compute and interpret a sample ACF;
• use PACF cut-offs as candidate-model evidence.

1. The stable object that ARMA models require
2. ACF: total linear memory
3. PACF: direct dependence after intermediate lags
4. Worked diagnostic: level, return, and volatility memory