Testing for Unit Roots in Time Series Data
Let Y satisfy the stochastic difference equation null for t = 1,2,…, where e are independent and identically distributed random variables with mean zero and variance σ 2 and the initial conditions ( Y −p+1 ,…, Y 0 ) are fixed constants. It is assumed that the process is invertible and that the true, but unknown, roots m 1 , m 2 ,…, m of null satisfy the hypothesis H : m 1 = … = m = 1 and | m | j = d + 1,…, p . We present a reparameterization of the model for Y that is convenient for testing the hypothesis H . We consider the asymptotic properties of (i) a likelihood ratio type “ F -statistic” for testing the hypothesis H , (ii) a likelihood ratio type t -statistic for testing the hypothesis H against the alternative H . Using these asymptotic results, we obtain two sequential testing procedures that are asymptotically consistent.
Volume (Year): 5 (1989)
Issue (Month): 02 (August)
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