This paper investigates limit theory for the likelihood analysis of
an I (2) cointegrated vector autoregressive (VAR) model in the presence of
deterministic shifts. A log likelihood ratio (log LR) test statistic for
integration indices is considered, and it is demonstrated that the
asymptotic distribution of the statistic is given in the form of a
generalised Dicky-Fuller type distribution. A log LR test statistic for
restrictions on long-run and slope coefficients is also investigated, and
it is proved that the statistic is asymptotically chi-square distributed.
Finally, an empirical analysis of macroeconomic data in Japan is performed
using the I(2) VAR model subject to a deterministic shift.

Program and Maps

Program and Maps

Program and Maps

要旨：The effort to lower the space barriers is in the core of what we call economic development, industrial structure transformation, and technological innovation like steam engine, motorcar, radio, TV, telephone, mobile phone etc. Owning and consuming them is not the ultimate purpose they serve. They exist to be used to spatially move human beings, commodities, or information. Human activities to lower spatial barriers, which macro-economics is apt to ignore, are nothing else than the dynamic process of economic development itself. To acquire a limited number and quantity of goods and services, we need to mobilize a set of space overcoming system.