In general in econometrics, especially in the area of financial markets, series are observed which indicate a non-stationary behavior. In the previous chapter we saw that econometric models, which are based on assumptions of rational expectations, frequently imply that the relevant levels of, for example, prices, follow a random walk. In order to handle these processes within the framework of the classical time series analysis, we must first form the differences in order to get a stationary process. We generalize the definition of a difference stationary process in the following definition.
White noise is, for example, , a random walk
. In only
a few cases processes are observed that are
with
This means that in most cases first differences are enough to form
a stationary process. In the following we assume that the observed
process
is
and we consider the transformed process
, i.e., we will concentrate on stationary
processes.