Testing for Breaks in Regression Models with Dependent Data

The paper examines a test for smoothness/breaks in a nonparametric regression model with dependent data. The test is based on the supremum of the difference between the one-sided kernel regression estimates. When the errors of the model exhibit strong dependence, we have that the normalization constants to obtain the asymptotic Gumbel distribution are data dependent and the critical values are difficult to obtain, if possible. This motivates, together with the fact that the rate of convergence to the Gumbel distribution is only logarithmic, the use of a bootstrap analogue of the test. We describe a valid bootstrap algorithm and show its asymptotic validity. It is interesting to remark that neither subsampling nor the sieve bootstrap will lead to asymptotic valid inferences in our scenario. Finally, we indicate how to perform a test for k breaks against the alternative of \(k+k_{0}\) breaks for some \(k_{0}\).