Spanning Trees and Bootstrap Reliability Estimation in Correlation-Based Networks

Tumminello, Michele; Coronnello, Claudia; Lillo, Fabrizio; Miccichè, Salvatore; Mantegna, Rosario N.

doi:10.1142/s0218127407018415

Cited by 145 publications

(128 citation statements)

References 55 publications

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“…The first condition is typically observed in the financial case, while the latter condition is always satisfied by the UPGMA and the WPGMA, while it could be violated in the Hausdorff method. When reversals are present in the dendrogram associated with the Hausdorff method, we remove such reversals using the minimum spanning tree associated with the hierarchical clustering procedure (Tumminello et al 2007a). Since our procedure generates positive definite matrices, they can be interpreted as correlation matrices.…”

Section: Agglomerative Hierarchical Clustering Estimatorsmentioning

confidence: 99%

When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

Pantaleo

Tumminello

Lillo

et al. 2011

Quantitative Finance

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The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of nine improved covariance estimation procedures using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between the estimation period T and the number of stocks N, on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than that obtained with the sample covariance method. This is particularly true when T/N is close to one. Moreover, many estimators reduce the fraction of negative portfolio weights, while little improvement is achieved in the degree of diversification. On the contrary, when short selling is not allowed and T > N, the considered methods are unable to outperform the sample covariance in terms of realized risk, but can give much more diversified portfolios than that obtained with the sample covariance. When T < N, the use of the sample covariance matrix and of the pseudo-inverse gives portfolios with very poor performance.Portfolio optimization, Correlation structures, Statistical methods, Econophysics,

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Section: Agglomerative Hierarchical Clustering Estimatorsmentioning

confidence: 99%

When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

Pantaleo

Tumminello

Lillo

et al. 2011

Quantitative Finance

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“…Some studies aimed to find relationships between MSTs and the single-linkage and average-linkage cluster analysis of the original graph. 39,40 In our study, we applied the average-linkage cluster analysis to the geodesic distance matrix of the MSTs rather than the original graph. We represented the results of the TAHC algorithm in the form of dendrograms, in which the nodes of the MSTs are depicted at the bottom.…”

Section: Discussionmentioning

confidence: 99%

Hierarchical clustering in minimum spanning trees

Hillebrand

Tewarie

et al. 2015

Chaos

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The identification of clusters or communities in complex networks is a reappearing problem. The minimum spanning tree (MST), the tree connecting all nodes with minimum total weight, is regarded as an important transport backbone of the original weighted graph. We hypothesize that the clustering of the MST reveals insight in the hierarchical structure of weighted graphs. However, existing theories and algorithms have difficulties to define and identify clusters in trees. Here, we first define clustering in trees and then propose a tree agglomerative hierarchical clustering (TAHC) method for the detection of clusters in MSTs. We then demonstrate that the TAHC method can detect clusters in artificial trees, and also in MSTs of weighted social networks, for which the clusters are in agreement with the previously reported clusters of the original weighted networks. Our results therefore not only indicate that clusters can be found in MSTs, but also that the MSTs contain information about the underlying clusters of the original weighted network. Clustering or community structure has been regarded as one of the most significant features of complex networks. The minimum spanning tree (MST) is the spanning tree in a weighted graph for which the sum of the weights of its constituting links is minimal. There are many different kinds of algorithms for identifying clusters in general networks, but a general definition and algorithm for the detection of clusters in trees has not been established. In our current study, we first define clusters in trees and propose a tree agglomerative hierarchical clustering (TAHC) method for the detection of clusters in MSTs. By detecting clusters in both artificial trees and the MSTs of two weighted social networks, we demonstrate that the clustering of the MSTs reveals the underlying clusters of the original weighted graphs.

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“…In order to distinguish between those chosen linkages which are undoubtedly the best ones from those which are chosen because they are slightly better than the other linkages connecting that node, we use the technique proposed by Efron (1979) and applied by Tumminello et al (2007) and Kantar et al (2011) to spot unreliable linkages. We create 1,000 random datasets picking, allowing repetitions, 762 days.…”

Section: Network Constructionmentioning

confidence: 99%

“…As the correlation matrix is dense and the resulting network would have an overwhelming amount of linkages, Mantegna suggests building a minimum spanning tree (Gower and Ross, 1969) which can give an overview of the structure without cycles, which is therefore very comprehensible for professionals. On the other hand, a minimum spanning tree's (MST) displayed information is partial, as it sacrifices for readability purposes some potentially strong relations hiding them; therefore, it is usually coupled with a linkage's reliability measure (Tumminello et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

The network of the Italian stock market during the 2008–2011 financial crises

Coletti

Murgia

2017

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Abstract.We build the network of the top 190 Italian quoted companies during the two financial crises of 2008-2009 (US credit crisis) and 2010-2011 (European sovereign debt crisis) and compare its structure to the pre-crises years, using both minimum spanning trees and the full network with thresholds. We also analyze the centrality and compactness of industry sectors. We find a general contraction of the network during the crises, both numerically due to stronger correlation as well as topologically, with the appearance of central dominant companies which attract the other ones into a very large cluster, dominated by financial institutions (commercial banks and insurance companies). In particular, we note the role of insurance behemoth Assicurazioni Generali, which rises from a pre-crises subordinate role to become the central company in the minimum spanning tree after the crises period. The few sectors which maintain compactness before and during the crises are utilities, publishing, and construction.

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Spanning Trees and Bootstrap Reliability Estimation in Correlation-Based Networks

Cited by 145 publications

References 55 publications

When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

Hierarchical clustering in minimum spanning trees

The network of the Italian stock market during the 2008–2011 financial crises

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