A general framework is proposed for (auto) regression non-parametric estimation of recurrent time series in a class of Hilbert Markov processes with a Lipschitz conditional mean. This includes various non-stationarities by relaxing usual dependence assumptions as mixing or ergodicity, which are...

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local...