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G. Marti et al.
a final footnote which serves both as an advice and a warning for future work and
applications:
One final comment on the method of analysis: this study has employed techniques that
rely on finite variances and stationary processes when there is considerable doubt about
the existence of these conditions. It is believed that a convincing argument has been made
for acceptance of the hypothesis that a small number of factors, market and industry, are
sufficient to explain the essential comovement of a large group of stock prices; it is possible,
however, that more satisfactory results could be obtained by methods that are distribution free.
Here we are thinking of a factor-analytic analogue to median regression and non-parametric
analysis of variance, where the measure of distance is something other than expected squared
deviation. In future research we would probably seriously consider investing some time in
the exploration of distribution free methods.
It is only but recently that researchers have started to focus on these shortcomings
as we will observe through the research contributions detailed in the next section.
10.3.2 Contributions for Improving the Methodology
To alleviate some of the shortcomings mentioned in the previous section, researchers
have mainly proposed alternative algorithms and enhanced distances. Some refinements of the methodology as a whole, alongside efforts to tackle the concerns about
statistical soundness, have been proposed.
On algorithms
Several alternative algorithms have been proposed to replace the minimum spanning
tree and its corresponding clusters:
• Average Linkage Minimum Spanning Tree (ALMST) [144]; Authors introduce
a spanning tree associated to the Average Linkage Clustering Algorithm (ALCA);
It is designed to remedy the unwanted chaining phenomenon of MST/SLCA.
• Planar Maximally Filtered Graph (PMFG) [3, 143] which strictly contains the
Minimum Spanning Tree (MST) but encodes a larger amount of information in its
internal structure.
• Directed Bubble Hierarchal Tree (DBHT) [131, 132] which is designed to
extract, without parameters, the deterministic clusters from the PMFG.
• Triangulated Maximally Filtered Graph (TMFG) [96]; Authors introduce
another filtered graph more suitable for big datasets.
• Clustering using Potts super-paramagnetic transitions [77]; When anti-correlations
occur, the model creates repulsion between the stocks which modify their clustering structure.
• Clustering using maximum likelihood [52, 53]; Authors define the likelihood of
a clustering based on a simple 1-factor model, then devise parameter-free methods
to find a clustering with high likelihood.
G. Marti et al.
a final footnote which serves both as an advice and a warning for future work and
applications:
One final comment on the method of analysis: this study has employed techniques that
rely on finite variances and stationary processes when there is considerable doubt about
the existence of these conditions. It is believed that a convincing argument has been made
for acceptance of the hypothesis that a small number of factors, market and industry, are
sufficient to explain the essential comovement of a large group of stock prices; it is possible,
however, that more satisfactory results could be obtained by methods that are distribution free.
Here we are thinking of a factor-analytic analogue to median regression and non-parametric
analysis of variance, where the measure of distance is something other than expected squared
deviation. In future research we would probably seriously consider investing some time in
the exploration of distribution free methods.
It is only but recently that researchers have started to focus on these shortcomings
as we will observe through the research contributions detailed in the next section.
10.3.2 Contributions for Improving the Methodology
To alleviate some of the shortcomings mentioned in the previous section, researchers
have mainly proposed alternative algorithms and enhanced distances. Some refinements of the methodology as a whole, alongside efforts to tackle the concerns about
statistical soundness, have been proposed.
On algorithms
Several alternative algorithms have been proposed to replace the minimum spanning
tree and its corresponding clusters:
• Average Linkage Minimum Spanning Tree (ALMST) [144]; Authors introduce
a spanning tree associated to the Average Linkage Clustering Algorithm (ALCA);
It is designed to remedy the unwanted chaining phenomenon of MST/SLCA.
• Planar Maximally Filtered Graph (PMFG) [3, 143] which strictly contains the
Minimum Spanning Tree (MST) but encodes a larger amount of information in its
internal structure.
• Directed Bubble Hierarchal Tree (DBHT) [131, 132] which is designed to
extract, without parameters, the deterministic clusters from the PMFG.
• Triangulated Maximally Filtered Graph (TMFG) [96]; Authors introduce
another filtered graph more suitable for big datasets.
• Clustering using Potts super-paramagnetic transitions [77]; When anti-correlations
occur, the model creates repulsion between the stocks which modify their clustering structure.
• Clustering using maximum likelihood [52, 53]; Authors define the likelihood of
a clustering based on a simple 1-factor model, then devise parameter-free methods
to find a clustering with high likelihood.