  In this paper, we develop a new sequential regression modeling approach for
data streams. Data streams are commonly found around us, e.g in a retail
enterprise sales data is continuously collected every day. A demand forecasting
model is an important outcome from the data that needs to be continuously
updated with the new incoming data. The main challenge in such modeling arises
when there is a) high dimensional and sparsity, b) need for an adaptive use of
prior knowledge, and/or c) structural changes in the system. The proposed
approach addresses these challenges by incorporating an adaptive L1-penalty and
inertia terms in the loss function, and thus called Inertial Regularization and
Selection (IRS). The former term performs model selection to handle the first
challenge while the latter is shown to address the last two challenges. A
recursive estimation algorithm is developed, and shown to outperform the
commonly used state-space models, such as Kalman Filters, in experimental
studies and real data.
