  In this paper the problem of forecasting high dimensional time series is
considered. Such time series can be modeled as matrices where each column
denotes a measurement. In addition, when missing values are present, low rank
matrix factorization approaches are suitable for predicting future values. This
paper formally defines and analyzes the forecasting problem in the online
setting, i.e. where the data arrives as a stream and only a single pass is
allowed. We present and analyze novel matrix factorization techniques which can
learn low-dimensional embeddings effectively in an online manner. Based on
these embeddings a recursive minimum mean square error estimator is derived,
which learns an autoregressive model on them. Experiments with two real
datasets with tens of millions of measurements show the benefits of the
proposed approach.
