Time Series and Stationarity

Works out what makes time series data structurally different from cross-sectional data: a stochastic process has an ensemble dimension (fixed time, varying realization, where distributions live) and a temporal dimension (fixed realization, varying time, where the data live), and a single history offers no replication at any one time point. Covers autocorrelation as the structure that substitutes for that missing replication, why stationarity is required before prediction is possible at all, strict vs. weak (covariance) stationarity and why practice targets the latter, ergodicity as a separate assumption from stationarity (with a worked example of a stationary but non-ergodic process, verified by simulation), and a taxonomy of how real series actually become non-stationary -- trends, level shifts, regime shifts, variance changes, and unit roots -- each with a different diagnostic signature. Closes by explaining why no single test can certify stationarity, previewing a dedicated future article on the tests themselves.