By Helmut Lütkepohl; Markus Krätzig
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Additional info for Applied time series econometrics
The recent empirical literature has found it useful to distinguish between the short- and long-run parts of a model. These parts are conveniently separated in a VECM by paying particular attention to a detailed modeling of the cointegration properties of the variables. Therefore, Chapter 3 emphasizes modeling of cointegrated series. In this analysis the results of preliminary unit root tests are of some importance. More generally, some univariate characteristics of the series form a basis for the choice of multivariate models and the analysis tools used at the systems level.
As another example consider German macroeconomic variables. Some of them refer to West Germany only 4 Helmut Lutkepohl ¨ before the German reunification and to all of Germany thereafter. Clearly, one could argue that the definitions of the relevant variables have changed over time. Another problem with the data offered in many databases is that they have been adjusted, modified, or transformed in some way. Seasonal adjustment is, for instance, a standard procedure that is often applied to data published by statistical agencies.
It appears to fluctuate randomly around a constant mean, and its variability is homogeneous during the observation period. Some correlation between consecutive values seems possible. In contrast, the second series, representing a German long-term interest rate, evolves more slowly, although its variability is also fairly regular. The sluggish, longer term movements are often thought of as a stochastic trend. The third series represents German gross national product (GNP). It appears to evolve around a deterministic polynomial trend, and, moreover, it has a distinct seasonal movement.
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