  When a series of (related) linear models has to be estimated it is often
appropriate to combine the different data-sets to construct more efficient
estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive
Lasso which can simultaneously do parameter estimation and model selection. We
show that for a time-course of high-dimensional linear models the convergence
rates of the Lasso and of the Adaptive Lasso can be improved by combining the
different time-points in a suitable way. Moreover, the Adaptive Lasso still
enjoys oracle properties and consistent variable selection. The finite sample
properties of the proposed methods are illustrated on simulated data and on a
real problem of motif finding in DNA sequences.
