Bootstrap test for breaks of a regression model with dependent data

Abstract. The paper describes and examines a test for breaks in a nonparametric regression function with dependent errors. We show that after normalization the limit distribution of the test is a Gumbel distribution. However, as (a) the normalization constants are model dependent and difficult to estimate and (b) the rate of convergence of the finite sample distribution of the statistic to the asymptotic one is very slow, see Hall (1979), inferences based on the asymptotic distribution may be difficult to perform or not be very reliable. For those reasons, we describe and examine the bootstrap analogue of the test by mean of bootstrapping the model in the ”frequency domain”, showing its asymptotic validity under suitable regularity conditions.