This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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 t-1 + 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 t-1 + e t and test H : ρ = 1 nonstationarity against H 1 : ρ < 1 This is exactly equivalent to the regression (x t- x t-1 ) = ( ρ- 1)x t-1 + e t = β x t-1 + e t and test H’ : β = 0 against H’ 1 : β < 0 a one-sided test However the ‘t-ratio’ for this regression t( β ) = β /SE( β ) 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 μ If x t is nonstationary x t- μ = x t-1- μ + e t so the mean drops out...
View Full Document
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