Factor models in high-dimensional time series
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Date
2013-03-20
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Abstract
High-dimensional time series may well be the most common type of dataset in the so-called
"big data" revolution, and have entered current practice in many areas, including
meteorology, genomics, chemometrics, connectomics, complex physics simulations, biological
and environmental research, finance and econometrics. The analysis of such datasets
poses significant challenges, both from a statistical as from a numerical point of view. The
most successful procedures so far have been based on dimension reduction techniques and,
more particularly, on high-dimensional factor models. Those models have been developed,
essentially, within time series econometrics, and deserve being better known in other areas.
In this paper, we provide an original time-domain presentation of the methodological
foundations of those models (dynamic factor models usually are described via a spectral
approach), contrasting such concepts as commonality and idiosyncrasy, factors and common
shocks, dynamic and static principal components. That time-domain approach emphasizes
the fact that, contrary to the static factor models favored by practitioners, the so-called general
dynamic factor model essentially does not impose any constraints on the data-generating
process, but follows from a general representation result.