In this book, there is a chapter titled Recurrent Models (you can see that chapter in Google books) but it's very short and some parts are not very clear to me. Recurrent Models seem to refer to a regression of the following form:
$$y_{k} = f(y_{k-m},..., y_{k-1},x_{k-m},..., x_{k-1}) \hspace{20mm}\text{for} \; k = m+1,....,n$$
However, I would like to get more information about this topic but maybe the name recurrent model is not a very common one, so I'm having a hard time getting more notes or books about it. Can anyone give me some pointers?
Thanks
I don't know what you need this for, but what this author calls 'recurrent' seems a general version of autoregressive (AR) or vector-autoregressive (VAR) models. While these, to my knowledge, are assumed linear in their evolution over time, I'm not sure if the more general functional relationship of this book's definition is actionable in practice. If you need to estimate something along these lines, you might want to start reading about these well-understood and investigated models. Here's the wiki link: http://en.wikipedia.org/wiki/Vector_autoregression. A good book covering this in great detail is Hamilton, Time Series analysis.
Edit (see comment below): I touched base with my gf. While not precisely under the name "recurrent models," she suggested to google "Real-time computing without stable states," and the researcher names Maass, Buonomano, and Jaeger; also a paper by Abbott&Sussillo on recurrent nets for computation. This is how 'recurrent' models are used in contemporary theoretical neuroscience, which may or may not be what you are interested in. There should be an introductory article on Scholarpedia, eg, http://www.scholarpedia.org/article/Echo_state_network.