distributions and critical values have been tabulated. In finite samples, a superior alternative to the use of these asymptotic critical value is to generate critical values from simulations. Multicointegration In practice, cointegration is often used for two series, but it is more generally applicable and can be used for variables integrated of higher order (to detect correlated accelerations or other second-difference effects). Multicointegration extends the cointegration technique beyond two variables, and occasionally to variables integrated at different orders. Variable shifts in long time series Tests for cointegration assume that the cointegrating vector is constant during the period of study. In reality, it is possible that the long-run relationship between the underlying variables change (shifts in the cointegrating vector can occur). The reason for this might be technological progress, economic crises, changes in the people's preferences and behaviour accordingly, policy or regime alteration, and organizational or institutional developments. This is especially likely to be the case if the sample period is long. To take this issue into account, tests have been introduced for cointegration with one unknown structural break, and tests for cointegration with two unknown breaks are also available. Bayesian inference Several Bayesian methods have been proposed to compute the posterior distribution of the number of cointegrating relationships and the cointegrating linear combinations. See also Error correction model Granger causality Stationary subspace analysis References Further reading An intuitive introduction to cointegration. Mathematical finance Time series