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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 = ρ x t1 + e t with ρ = 1 Hence to test whether x t is a random walk (with zero mean), we could estimate x t = ρ x t1 + e t and test H : ρ = 1 nonstationarity against H 1 : ρ < 1 This is exactly equivalent to the regression (x t x t1 ) = ( ρ 1)x t1 + e t = β x t1 + e t and test H’ : β = 0 against H’ 1 : β < 0 a onesided test However the ‘tratio’ for this regression t( β ) = β /SE( β ) 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 μ If x t is nonstationary x t μ = x t1 μ + e t so the mean drops out...
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This note was uploaded on 03/07/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.
 Spring '10
 Cowell
 Economics

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