Nonstationary Systems with Integrated and Cointegrated Variables

Abstract

In Parts I and II we have considered stationary, stable systems. As stated in Chapter 2, a process is stationary if it has time invariant first and second moments. This implies that there are no trends (trending means) or shifts in the mean or in the covariances or specific seasonal patterns. Of course, trends and seasonal fluctuations are quite common in practice. For instance, the original investment, income, and consumption data used in many previous examples have trends (see Figure 3.1). Thus, if interest centers on analyzing the original variables rather than the rates of change it is necessary to have models that accommodate the nonstationary features of the data. In Chapter 2 it is demonstrated that a stable process is stationary. Unstable nonstationary processes will be considered in this chapter and other types of nonstationarities will be treated in the next chapters. We shall begin with a brief summary of important characteristics of specific unstable processes.