  We propose a novel methodology to define, analyze and forecast market states.
In our approach market states are identified by a reference sparse precision
matrix and a vector of expectation values. In our procedure, each multivariate
observation is associated with a given market state accordingly to a
minimization of a penalized Mahalanobis distance. The procedure is made
computationally very efficient and can be used with a large number of assets.
We demonstrate that this procedure is successful at clustering different states
of the markets in an unsupervised manner. In particular, we describe an
experiment with one hundred log-returns and two states in which the methodology
automatically associates states prevalently to pre- and post- crisis periods
with one state gathering periods with average positive returns and the other
state periods with average negative returns, therefore discovering
spontaneously the common classification of `bull' and `bear' markets. In
another experiment, with again one hundred log-returns and two states, we
demonstrate that this procedure can be efficiently used to forecast off-sample
future market states with significant prediction accuracy. This methodology
opens the way to a range of applications in risk management and trading
strategies in the context where the correlation structure plays a central role.
