Stationarity and Autocorrelation
When statistical properties hold across time, and when they don't.
A time series is stationary if its statistical properties don't change over time. Strict stationarity requires the full joint distribution to be time-invariant; weak (covariance) stationarity requires constant mean, constant variance, and an autocovariance that depends only on the lag :
Most practical work uses weak stationarity. The autocorrelation function (ACF) summarizes how observations at different lags relate.
Most financial price series are non-stationary — they drift and have time-varying volatility. Returns are usually closer to stationary, which is why we model returns rather than levels. Tests like the Augmented Dickey-Fuller (ADF) check for unit roots that signal non-stationarity.