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Applied Econometric Times Series, 3rd Edition by Walter Enders

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CHAPTER 4

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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:

  1. 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.
  2. 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.
  3. 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.
  4. Illustrate the lack of power of the standard Dickey–Fuller tests. Unit ...

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