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The method of cointegration in regression analysis is based on an assumptionof stationary increments. Stationary increments with fixed time lag are calledintegration I(d). A class of regression models where cointegration works wasidentified by Granger and yields the ergodic behavior required for equilibriumexpectations in standard economics. Detrended finance market returns aremartingales, and martingales do not satisfy regression equations. We extend thestandard discussion to discover the class of detrended processes beyondstandard regression models that satisfy integration I(d). In the language ofeconometrics, the models of interest are unit root models, meaning martingales.Typical martingales do not have stationary increments, and those that dogenerally do not admit ergodicity. Our analysis leads us to comment on the lackof equilibrium observed earlier between FX rates and relative price levels.

Integration I(d) of Nonstationary Time Series: Stationary and nonstationary increments