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Time series econometrics is centred around the representation theorems from which one can evict the integration and cointegration characteristics of the solutions for the vector autoregressive (VAR) models.

Such theorems, along the path established by Engle and Granger and by Johansen and his school, have promoted the parallel development of an “ad hot” analytical implement — although not always fully settled.

The present chapter, by reworking and expanding some recent contributions due to Faliva and Zoia, provides in an organic fashion an algebraic setting based upon several interesting results on inversion by parts and on Laurent series expansion for the reciprocal of a matrix polynomial in a deleted neighbourhood of a unitary root. Rigorous and efficient, such a technique allows for a quick and new reformulation of the representation theorems as it will become clear in Chapter 3.

This chapter introduces the basic notions regarding the multivariate stochastic processes. In particular, the reader will find the definitions of stationarity and of integration which are of special interest for the subsequent developments. The second part deals with principle stationary processes. The third section shows the way to integrated processes and takes a glance at cointegration. The last section deals with integrated and cointegrated processes and related topics of major interest. An appendix on the rôle of cointegration completes this chapter.

This chapter introduces the basic notions regarding the multivariate stochastic processes. In particular, the reader will find the definitions of stationarity and of integration which are of special interest for the subsequent developments. The second part deals with principle stationary processes. The third section shows the way to integrated processes and takes a glance at cointegration. The last section deals with integrated and cointegrated processes and related topics of major interest. An appendix on the rôle of cointegration completes this chapter.