On the oversized problem of Dickey-Fuller-type tests with GARCH errors

Abstract

This paper examines the finite-sample size of a class of Dickey-Fuller-type tests in the presence of GARCH errors, with and without the influence of initial conditions of the underlying simulated path. Oversizing is observed for all tests when the GARCH process is nearly degenerate and the volatility parameter is large, but the degree of size distortion varies across tests and is contingent on the initial condition. The result due to the initial effect is linked to the size distortion caused by a sequence of small downward variance breaks arising in the early stage of the underlying process.