Forecasting Market States

Abstract

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 minimisation 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 successfull 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.

Market structure dynamics during COVID-19 outbreak

“…We used the unsupervised clustering methodology described in (1) to automatically extract four inherent marketstructures associated with a set of 623 equities continuously traded in the US market during the period from February 1999 to March 20, 2020. The clustering was performed by maximising the following adjusted log-likelihood:…”

“…where Xt ∈ R n,1 is the vector of log-returns at time t; 1 is the vector of the expected values for cluster k; J k ∈ R n,n is the sparse precision matrix for cluster k computed via the LoGo method (see (2, 3)); γ is a parameter penalizing state switching. In the present analysis we use γ = 100, but results are consistent across a large range of values of this parameter.…”

Dynamic Portfolio Optimization with Inverse Covariance Clustering

“…After clustering, the precision matrix of each state is estimated under a Toeplitz constraint. Inspired by TICC, Procacci and Aste in 2020 [6] proposed a closed related methodology names Inverse Covariance Clustering (ICC). This approach provides a point clustering of observations also enforcing temporal consistency by penalizing switching between states.…”

“…In this paper, we provide an algorithm termed Inverse Covariance Clustering-Portfolio Optimization (ICC-PO) to address the non-stationarity problem, by identifying the inherent market states and forecast the most likely future state. The Inverse Covariance Clustering (ICC) [6] is a novel temporal clustering method for market states clustering. In this paper we propose to make use of this temporal clustering classification, constructing different optimal portfolios associated with two ICC market state clusters.…”

Hierarchies in communities of UK stock market from the perspective of Brexit

“…However, cluster analysis of a process, such as Brexit, which has a high impact on both global and local markets, is insufficient to perform only on minimum spanning topologies. Moreover, richer topologies such as planar maximally filtered graphs [43,45] and triangulated maximally filtered graphs [32,40] encode more detailed information about topological changes in financial markets through out crisis periods.…”