Forecasting Market States

We propose a novel methodology to define, analyse 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 to a given market state accordingly to a penalized likelihood maximization. The procedure is made computationally very efficient and can be used with a large number of assets. We demonstrate that this procedure successfully classifies 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 one state to periods with average positive returns and the other state to 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 where the correlation structure plays a central role