The presented paper aims to analyse both statistical and economic aspects of the model with I(2) variables. The statistical foundations of such models are introduced. The enlargement of possible statistical interpretation is discussed. The economic interpretation of both VECM parameters and common stochastic trends representation is considered in the I(2) domain. The returns of I(2) approach in terms of stock-flows, nominal-real analysis and diasggregation into both long-, short and even medium-run analysis are proved. Potential complications under reflecting I(3) variables are presented.

The paper analyses the consequences of structural change in the presenceof non-stationary stochastic processes I(1) or I(2). The structural change mayconcern the deterministic structure (in particular, the trend and the constantterm) as well as the process generating the stochastic part. The focus of thepaper is on the case of a discrete change in a regime for which the momentof switch is known. A change in the deterministic part does not alter thecharacter of the cointegration relationships but its consequences for cotrendingand cobreaking are interesting. The consequences of a change in the stochasticpart are more complex, because then the stochastic process as well as thedeterministic structure of the VECM are modified. The restrictions are analysedfor both cases.