  Varying coefficient models have numerous applications in a wide scope of
scientific areas. While enjoying nice interpretability, they also allow
flexibility in modeling dynamic impacts of the covariates. But, in the new era
of big data, it is challenging to select the relevant variables when there are
a large number of candidates. Recently several work are focused on this
important problem based on sparsity assumptions; they are subject to some
limitations, however. We introduce an appealing forward variable selection
procedure. It selects important variables sequentially according to a sum of
squares criterion, and it employs an EBIC- or BIC-based stopping rule. Clearly
it is simple to implement and fast to compute, and it possesses many other
desirable properties from both theoretical and numerical viewpoints. We
establish rigorous selection consistency results when either EBIC or BIC is
used as the stopping criterion, under some mild regularity conditions. Notably,
unlike existing methods, an extra screening step is not required to ensure
selection consistency. Even if the regularity conditions fail to hold, our
procedure is still useful as an effective screening procedure in a less
restrictive setup. We carried out simulation and empirical studies to show the
efficacy and usefulness of our procedure.
