Reduced-Rank and Nonstationary Co-Integrated Models

Abstract

In this chapter we present some additional topics concerning the modeling of vector time series. These include the examination of models which incorporate special structure in their parameterization, in particular, the nested reduced-rank models, which attempt to cope with the problem of the high dimensionality of the parameters in the vector models. Model specification methods, based on partial canonical correlation analysis, and parameter estimation will be presented for the nested reduced-rank AR models. We also consider estimation and testing issues relating to multivariate nonstationary models that contain unit roots in their AR operator, and the associated concept of cointegration among the components of a nonstationary vector process. Multiplicative seasonal vector ARMA models will be discussed as an additional special topic in this chapter.