An Autoregressive Model with Conditional Heterogeneity: a Nesting Model for Unit Root Testing

The main objective of this paper is to shed light on the problem of low power for the Dickey-Fuller type unit root tests. It is argued that the low power is primarily due to the non-nestedness of the Autoregressive (AR(1)) and the Unit Root (UR(1)) models. The paper proposes an AR(1) model with Conditional Heterogeneity (ARCHET(1)) which parametrically encompasses the UR(1) model. A number of simulations are used to demonstrate that, in the context of the ARCHET(1) model, the Likelihood ratio and Lagrange Multiplier tests have impressive power for alternatives close to the unit root. For instance, the power of the LR test is greater than 90 for ∈[095 10) and =100 compared to 30 for the Dickey-Fuller type tests.