MODELS WITH TREND
Inspection of the autocorrelation function serves as a rough indicator of whether a trend is present in a series. A slowly decaying ACF is indicative of a large characteristic root, a true unit root process, or a trend-stationary process. Formal tests can help determine whether a system contains a trend and whether the trend is deterministic or stochastic. However, the existing tests have difficulty distinguishing between near–unit root and unit root processes. This chapter has five aims:
- Formalize simple models of variables with a time-dependent mean. A trend can be completely deterministic or may contain stochastic components. It is essential to properly model the trend if you intend to do any hypothesis testing or long-term forecasting.
- Develop and illustrate the Dickey–Fuller and augmented Dickey–Fuller tests for the presence of a unit root. Several variants of the test are presented, including a test for seasonal unit roots. In order to develop the test statistics it is necessary to understand the nature of Monte Carlo experiments.
- Consider tests for unit roots in the presence of structural change. Structural change can complicate the tests for trends; a policy regime change can result in a structural break that makes an otherwise stationary series appear to be nonstationary.
- Illustrate the lack of power of the standard Dickey–Fuller tests. Unit ...