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