Stationarity and time series

Most statistics assume your data points are independent draws from one fixed distribution. Market data violates this badly: observations are ordered in time and each depends on the last. That is the domain of time-series analysis.

Stationarity — the precondition

A series is stationary if its statistical properties (mean, variance, autocorrelation) do not change over time. Most time-series models require stationarity to be valid.

Raw prices are emphatically not stationary — they trend, drift and wander. A model fit to a rising price series learns the trend, not the dynamics, and falls apart when the trend changes.

The standard fix: differencing

Quants transform prices into something stationary, almost always by taking returns (the difference of log prices). A price that wanders becomes a return series that hovers around a roughly constant mean. Tests like the Augmented Dickey-Fuller (ADF) test formally check whether a series is stationary.

Autocorrelation

Autocorrelation measures how a series correlates with its own past values at various lags. It answers: does today's return tell you anything about tomorrow's? For most liquid assets, return autocorrelation is famously close to zero — markets are almost efficient — but small, exploitable patterns persist, especially in volatility and at certain horizons.

Why this matters for any predictor

If you feed a non-stationary series into a model and validate it naively, you will get spectacular backtests that mean nothing. Half the discipline of time-series modelling is making the data stationary first, and respecting time order when you test — a point the validation chapter hammers home.