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# ch18 - Testing for Unit Roots Consider an AR(1 yt = yt-1 et...

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Economics 20 - Prof. Anderson 1 Testing for Unit Roots Consider an AR(1): y t = α + ρ y t-1 + e t Let H 0 : = 1, (assume there is a unit root) Define θ = – 1 and subtract y t-1 from both sides to obtain y t = + y t-1 + e t Unfortunately, a simple t-test is inappropriate, since this is an I(1) process A Dickey-Fuller Test uses the t-statistic, but different critical values

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Economics 20 - Prof. Anderson 2 Testing for Unit Roots (cont) We can add p lags of y t to allow for more dynamics in the process Still want to calculate the t-statistic for θ Now it’s called an augmented Dickey- Fuller test, but still the same critical values The lags are intended to clear up any serial correlation, if too few, test won’t be right
Economics 20 - Prof. Anderson 3 Testing for Unit Roots w/ Trends If a series is clearly trending, then we need to adjust for that or might mistake a trend stationary series for one with a unit root Can just add a trend to the model Still looking at the t-statistic for θ , but the critical values for the Dickey-Fuller test change

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Economics 20 - Prof. Anderson
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ch18 - Testing for Unit Roots Consider an AR(1 yt = yt-1 et...

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