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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 t-1 + e t with = 1 Hence to test whether x t is a random walk (with zero mean), we could estimate x t = x t-1 + e t and test H : = 1 nonstationarity against H 1 : < 1 This is exactly equivalent to the regression (x t- x t-1 ) = ( - 1)x t-1 + e t = x t-1 + e t and test H : = 0 against H 1 : < 0 a one-sided test However the t-ratio for this regression t( ) = /SE( ) has a non-standard 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 Dickey-Fuller test Testing the bond price for nonstationarity Using deviations from mean (so x t has zero mean) x t- x t-1 = -0.0384x t-1 + e t t-ratio on x t-1 = -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 non-zero mean Suppose x t has a non-zero mean If x t is nonstationary x t- = x t-1- + e t so the mean drops out...
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- Spring '10