Overview — Nonstationarity, Unit Roots, and Cointegration

A regression of two trending price levels can produce an impressive $R^2$, tiny reported $p$-values, and no economic relation at all. That failure matters directly to a relative-value desk: a hedge ratio estimated from unrelated random walks does not create a mean-reverting spread. This topic separates permanent stochastic trends from genuine long-run equilibria, then turns a verified equilibrium into a trading or forecasting model.

By the end of this note you should be able to:

• distinguish an I(1) random walk from a stationary I(0) process and recognise spurious level regressions;
• select and interpret Dickey--Fuller, ADF, and Phillips--Perron unit-root tests;
• test a bivariate long-run relation with Engle--Granger and represent it with an error-correction model;
• determine the number of long-run relations in a multivariate system using Johansen's rank tests;
• connect a cointegrated spot--futures pair or equity pair to an implementable spread model.

1. Contents
2. The big picture