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Unformatted text preview: 1 Testing time series for unit roots We know that a random walk is a particular type of AR(1) process x t = x t1 + e t with = 1 Hence to test whether x t is a random walk (with zero mean), we could estimate x t = x t1 + e t and test H : = 1 nonstationarity against H 1 : < 1 This is exactly equivalent to the regression (x t x t1 ) = (  1)x t1 + e t = x t1 + e t and test H : = 0 against H 1 : < 0 a onesided test However the tratio for this regression t( ) = /SE( ) has a nonstandard distribution (not a standard t distribution) Test procedure derived by Dickey/Fuller: compares t statistic with special critical values which are tabulated in Table 1 of Handout An example of the DickeyFuller test Testing the bond price for nonstationarity Using deviations from mean (so x t has zero mean) x t x t1 = 0.0384x t1 + e t tratio on x t1 = 1.381 (5% CV 1.95) We cannot reject H : this implies deviations in bond price are a random walk, as expected if speculators are rational 2 Testing series with a nonzero mean Suppose x t has a nonzero mean If x t is nonstationary x t = x t1 + e t so the mean drops out...
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 Spring '10
 Cowell
 Economics

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