CFDP 1475

Uniform Limit Theory for Stationary Autoregression


Publication Date: July 2004

Pages: 9


First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient ρ = ρn in [0,1) provided (1 - ρn)n approaches infinity. This extends existing Gaussian limit theory by allowing for values of stationary rho that include neighbourhoods of unity provided they are wider than (n1), even by a slowly varying factor. Rates of convergence depend on rho and are at least squareroot of /n but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed ρ.


Autoregression, Gaussian limit theory, local to unity, uniform limit

JEL Classification Codes: C22

See CFP: 1166