Regression with Autocorrelated Errors Using Design-Adapted Haar Wavelets

We present some theoretical results on semi-parametric regression models in the presence of autocorrelated errors using design-adapted Haar wavelets. We prove that the risks for the linear and nonlinear estimators are asymptotically almost minimax when the errors have absolutely summable autocovariances. For the nonlinear estimator, we also need a strong mixing property with a specific coefficient and a condition on the errors' higher-order moments. Some simulations ilustrate the theoretical achievements.