A primer on statistically validated networks

Miccichè, Salvatore; Mantegna, Rosario Nunzio

doi:10.48550/arxiv.1902.07074

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…It is often applied to financial correlation matrices due to its lack of assumptions on the underlying distribution. Statistical validation—which constitutes a generalisation of simpler thresholding methods—has been used to establish the significance of edges in correlation matrices, with applications to economics and finance as well as to other fields [ 11 , 12 , 13 , 14 , 15 ]. Statistical validation can be implemented by comparing the empirical correlations with null-hypothesis correlations generated from time-series randomized over the time dimension to remove dependency.…”

Section: Introductionmentioning

confidence: 99%

Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

Turiel

Barucca

Aste

2022

Entropy

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We introduce simplicial persistence, a measure of time evolution of motifs in networks obtained from correlation filtering. We observe long memory in the evolution of structures, with a two power law decay regimes in the number of persistent simplicial complexes. Null models of the underlying time series are tested to investigate properties of the generative process and its evolutional constraints. Networks are generated with both a topological embedding network filtering technique called TMFG and by thresholding, showing that the TMFG method identifies high order structures throughout the market sample, where thresholding methods fail. The decay exponents of these long memory processes are used to characterise financial markets based on their efficiency and liquidity. We find that more liquid markets tend to have a slower persistence decay. This appears to be in contrast with the common understanding that efficient markets are more random. We argue that they are indeed less predictable for what concerns the dynamics of each single variable but they are more predictable for what concerns the collective evolution of the variables. This could imply higher fragility to systemic shocks.

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Section: Introductionmentioning

confidence: 99%

Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

Turiel

Barucca

Aste

2022

Entropy

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“…It is often applied to financial correlation matrices due to its lack of assumptions on the underlying distribution. Statistical validation -which constitutes a generalisation of simpler thresholding methods -has been used to establish the significance of edges in correlation matrices, with applications to economics and finance as well as other fields (8)(9)(10)(11). Statistical validation can be implemented by comparing empirical networks with random networks from constrained randomisations which generate weighted ensembles of null models and allow to quantify the significance of observed realisations with respect to the ensemble statistics of the null constrained model.…”

Section: Introductionmentioning

confidence: 99%

Simplicial persistence of financial markets: filtering, generative processes and portfolio risk

Turiel,

Barucca,

Aste

2020

Preprint

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We introduce simplicial persistence, a measure of time evolution of network motifs in subsequent temporal layers. We observe long memory in the evolution of structures from correlation filtering, with a two regime power law decay in the number of persistent simplicial complexes. Null models of the underlying time series are tested to investigate properties of the generative process and its evolutional constraints. Networks are generated with both TMFG filtering technique and thresholding showing that embedding-based filtering methods (TMFG) are able to identify higher order structures throughout the market sample, where thresholding methods fail. The decay exponents of these long memory processes are used to characterise financial markets based on their stage of development and liquidity. We find that more liquid markets tend to have a slower persistence decay. This is in contrast with the common understanding that developed markets are more random. We find that they are indeed less predictable for what concerns the dynamics of each single variable but they are more predictable for what concerns the collective evolution of the variables. This could imply higher fragility to systemic shocks.

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“…Correlation networks [2] and network filtering techniques applied to the study of financial assets have recently gained wide attention [3][4][5][6][7][8][9][10]. These methods show that meaningful taxonomy of financial assets is identifiable from these sparse network structures.…”

Section: Introductionmentioning

confidence: 99%

Sector Neutral Portfolios: Long Memory Motifs Persistence in Market Structure Dynamics

Turiel

Aste

2019

SSRN Journal

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We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We observe long-memory processes in these structures in the form of power law decays in the number of persistent motifs. The decays then transition to a plateau regime with a power-law decay with smaller exponent. We demonstrate that identifying persistent motifs allows for forecasting and applications to portfolio diversification. Balanced portfolios are often constructed from the analysis of historic correlations, however not all past correlations are persistently reflected into the future. Sector neutrality has also been a central theme in portfolio diversification and systemic risk. We present an unsupervised technique to identify persistently correlated sets of stocks. These are empirically found to identify sectors driven by strong fundamentals.Applications of these findings are tested in two distinct ways on four different markets, resulting in significant reduction in portfolio volatility. A persistence-based measure for portfolio allocation is proposed and shown to outperform volatility weighting when tested out of sample.

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A primer on statistically validated networks

Cited by 3 publications

References 21 publications

Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

Simplicial persistence of financial markets: filtering, generative processes and portfolio risk

Sector Neutral Portfolios: Long Memory Motifs Persistence in Market Structure Dynamics

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