Characteristics of Time Series

The first step in building dynamic econometric models entails a detailed analysis of the characteristics of the individual time series variables involved. Such an analysis is important because the properties of the individual series have to be taken into account in modeling the data generation process (DGP) of a system of potentially related variables.

Some important characteristics of time series can be seen in the example series plotted in Figure 2.1. The first series consists of changes in seasonally adjusted U.S. fixed investment. 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. In addition there is a level shift in the third quarter of 1990. This shift is due to a redefinition of the series, which refers to West Germany only until the second quarter of 1990 and to the unified Germany afterwards. Although German reunification took place officially in October 1990, many economic time series were adjusted already on 1 July of that year, the date of the monetary unification. Finally, the last series in Figure 2.1 represents the daily DAFOX returns from 1985 to 1996. The DAFOX is a German stock index.