10 Correlations, Hierarchies, Networks and Clustering
251
strained by prior (hierarchical) market partition (e.g. into sectors); these principal
components are thus more stable and interpretable.
• Preprocessing of the time series:
– Subtract the market mode before performing a cluster or network analysis on
the returns [17],
– Encode both rank statistics and a distribution histogram of the returns into a
representative vector [37],
– Fit an ARMA(p,q)-FIEGARCH(1,d,1)-cDCC process (econometric preprocessing) to obtain dynamic correlations instead of the common approach of
rolling window Pearson correlations [128],
– Use a clustering of successive correlation matrices to infer a market state [59,
100, 115, 123, 136].
• Clustering of the time series based on parameters of estimated models:
– using coefficients of GARCH processes [110]
– using a Wasserstein distance between probability distributions obtained from a
time series change-point model [152]
• Use of other types of networks: threshold networks [109], influence networks
[50], partial-correlation networks [70, 72], Granger causality networks [14, 151],
cointegration-based networks [141], bipartite networks [149], multilayer networks
[8, 34], Bayesian networks and other probabilistic graphical models [36], etc.
• Understanding of the drivers of synchronous correlations using the properties of the
collective stock dynamics at shorter time scales [33] by using directed networks
of lagged correlations [32, 33].
10.4 Dynamics of Correlations, Hierarchies, Networks
and Clustering
Many of the empirical studies are based on the whole period available from the
data. Some researchers have started to investigate the dynamics of the empirical
correlations, and also the hierarchies, networks and clusters extracted from them (cf.
[108] as one of the earliest work). This dynamic setting which has the potential to
track changes of the market structure is more interesting for practitioners (e.g. risk
managers, traders, regulatory agencies). This research is still in its infancy and we
think its results are still hardly exploitable in practice. For instance, an interesting
but difficult question is the following: Are changes in the correlation structure due
to statistical noise and data artifacts or do they provide a real signal?
No predominant methodology has emerged for now but the naive one which
consists in:
251
strained by prior (hierarchical) market partition (e.g. into sectors); these principal
components are thus more stable and interpretable.
• Preprocessing of the time series:
– Subtract the market mode before performing a cluster or network analysis on
the returns [17],
– Encode both rank statistics and a distribution histogram of the returns into a
representative vector [37],
– Fit an ARMA(p,q)-FIEGARCH(1,d,1)-cDCC process (econometric preprocessing) to obtain dynamic correlations instead of the common approach of
rolling window Pearson correlations [128],
– Use a clustering of successive correlation matrices to infer a market state [59,
100, 115, 123, 136].
• Clustering of the time series based on parameters of estimated models:
– using coefficients of GARCH processes [110]
– using a Wasserstein distance between probability distributions obtained from a
time series change-point model [152]
• Use of other types of networks: threshold networks [109], influence networks
[50], partial-correlation networks [70, 72], Granger causality networks [14, 151],
cointegration-based networks [141], bipartite networks [149], multilayer networks
[8, 34], Bayesian networks and other probabilistic graphical models [36], etc.
• Understanding of the drivers of synchronous correlations using the properties of the
collective stock dynamics at shorter time scales [33] by using directed networks
of lagged correlations [32, 33].
10.4 Dynamics of Correlations, Hierarchies, Networks
and Clustering
Many of the empirical studies are based on the whole period available from the
data. Some researchers have started to investigate the dynamics of the empirical
correlations, and also the hierarchies, networks and clusters extracted from them (cf.
[108] as one of the earliest work). This dynamic setting which has the potential to
track changes of the market structure is more interesting for practitioners (e.g. risk
managers, traders, regulatory agencies). This research is still in its infancy and we
think its results are still hardly exploitable in practice. For instance, an interesting
but difficult question is the following: Are changes in the correlation structure due
to statistical noise and data artifacts or do they provide a real signal?
No predominant methodology has emerged for now but the naive one which
consists in: