10 Correlations, Hierarchies, Networks and Clustering
253
using daily returns, for N = 25 (Tel-Aviv stock market), and N = 455 (from
S&P 500)). They also propose a 3D visualization to monitor the configuration
of stocks using a 3D PCA.
– Reference [98] notices three regime shifts during the period 1989-2011 by monitoring eigenvalues and eigenvectors of the empirical correlation matrices (estimated using quarterly recorded prices from the US housing market; T = 60,
N = 51, the number of US states).
• the dynamics of the MST and other hierarchical trees:
Using summary statistics:
– The MST which evolves over time is monitored using summary statistics (also
called topological features) [107] such as the normalized tree length [108], the
mean occupation layer [108], the tree half-life [108], a survival ratio of the
edges [66, 106, 128], node degree, strength [128], eigenvector, betweenness
[138], closeness centrality [128], the agglomerative coefficient [97].
– Using these statistics, [108] notices that:
the MST strongly shrinks during a stock market crisis,
the optimal Markowitz portfolio lies practically at all times on the outskirts
of the tree,
the normalized tree length and the investment diversification potential are
very strongly correlated.
– And [128] notices that in the Asia-Pacific stock market:
the DST (a dynamic MST built from dynamic correlations) shrinks over time,
Hong Kong is found to be the key financial market,
the DST has a significantly increased stability in the last few years,
the removal of the key player has two effects: there is no clear key market
any longer and the stability of the DST significantly decreases.
– In [67], authors observe that for the Japanese and Korean stock markets, there
is a decrease of grouping by industry categories.
Using distances or similarity measures between successive dendrograms:
– Cophenetic correlation coefficient. In [97], authors propose a cophenetic analysis of public debt dendrograms in the European Union (N = 29 countries)
computed using Pearson correlation of quarterly debt-to-GDP ratios between
2000 Q1 and 2014 Q1 (T = 57) with a sliding window of size w = 15.
• the dynamics of clusters:
– The paper [75] finds that the cluster structures are more stable during crises
(using the p-median problem, an alternative clustering methodology).
253
using daily returns, for N = 25 (Tel-Aviv stock market), and N = 455 (from
S&P 500)). They also propose a 3D visualization to monitor the configuration
of stocks using a 3D PCA.
– Reference [98] notices three regime shifts during the period 1989-2011 by monitoring eigenvalues and eigenvectors of the empirical correlation matrices (estimated using quarterly recorded prices from the US housing market; T = 60,
N = 51, the number of US states).
• the dynamics of the MST and other hierarchical trees:
Using summary statistics:
– The MST which evolves over time is monitored using summary statistics (also
called topological features) [107] such as the normalized tree length [108], the
mean occupation layer [108], the tree half-life [108], a survival ratio of the
edges [66, 106, 128], node degree, strength [128], eigenvector, betweenness
[138], closeness centrality [128], the agglomerative coefficient [97].
– Using these statistics, [108] notices that:
the MST strongly shrinks during a stock market crisis,
the optimal Markowitz portfolio lies practically at all times on the outskirts
of the tree,
the normalized tree length and the investment diversification potential are
very strongly correlated.
– And [128] notices that in the Asia-Pacific stock market:
the DST (a dynamic MST built from dynamic correlations) shrinks over time,
Hong Kong is found to be the key financial market,
the DST has a significantly increased stability in the last few years,
the removal of the key player has two effects: there is no clear key market
any longer and the stability of the DST significantly decreases.
– In [67], authors observe that for the Japanese and Korean stock markets, there
is a decrease of grouping by industry categories.
Using distances or similarity measures between successive dendrograms:
– Cophenetic correlation coefficient. In [97], authors propose a cophenetic analysis of public debt dendrograms in the European Union (N = 29 countries)
computed using Pearson correlation of quarterly debt-to-GDP ratios between
2000 Q1 and 2014 Q1 (T = 57) with a sliding window of size w = 15.
• the dynamics of clusters:
– The paper [75] finds that the cluster structures are more stable during crises
(using the p-median problem, an alternative clustering methodology).