On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent data

Motivated by the huge success of deep neural networks in applications (see, e.g., Schmidhuber (2015), Rawat and Wang (2017), Hewamalage, Bergmeir and Bandara (2020) and the literature cited therein) there is nowadays a strong interest in showing theoretical properties of such estimates. In the last years many new results concerning deep feedforward neural network estimates have been derived (cf., e.g., Eldan and Shamir (2016), Lu et al. (2020), Yarotsky (2018) and Yarotsky and Zhevnerchuk (2019) concerning approximation properties or Kohler and Krzyżak (2017), Bauer and Kohler (2019) and Schmidt-Hieber (2020) concerning statistical properties of these estimates).