Lecture 23 The Dickey-Fuller Test We have seen that
Download 274.11 Kb.
|
| Lecture 23 – The Dickey-Fuller Test
We have seen that the dynamic behavior of I(1) processes is quite different from the behavior of I(0) processes the way we go about defining and estimating the trend and cyclical components of a time series may depend on whether we assume the series is (trend) stationary or difference stationary. regressions with difference stationary variables need special care. For these reasons we might be interested in testing the null hypothesis of a unit root against the stationary or trend-stationary alternative. Consider the following AR(1) model for yt: yt = ρyt-1 + εt , εt ~ iid (0,σ2) -1 < ρ < 1 If ρ < 1, yt ~ I(0), mean 0 and var σ2/(1-ρ2) If ρ = 1, yt ~ I(1), a random walk The OLS estimator of ρ is consistent for all ρ; it is super-consistent when ρ = 1. The OLS t-statistic 
where  is the OLS s.e. of ρ-hat,
is asymptotically standard normal when Directory: classes classes -> Ch. 1 Competing with Operations. 2, 3, 4 on p27-28 classes -> 1Introduction classes -> Unit 1: Exploration and Colonization classes -> Ap united States History Course Description classes -> Industrial Revolution classes -> 1–xx. The Redevelopment of a Warm Core Structure in Erin: a case of Inland Tropical Storm Formation classes -> Unit 7 Notes Organizer: C. Increasing Influences and Challenges); D. Challenges at Home & Abroad The United States in a Changing World (wwi) classes -> Unit 1: Colonial America (Twelve Days) Standard 1-2 Unit 2: Revolution (Ten Days) classes -> Review of Chapters 1-3, 8, and the appendix classes -> Seasonal Influences upon and Long-Term Trends in the Length of the Atlantic Hurricane Season Download 274.11 Kb. Share with your friends:
|