Time Series Clustering

For risk benchmarking, the user of the website is provided with tools for hierarchical clustering by various methods on the basis of time series data mining, with the use of either classic metrics (including Pearson correlation) or time series similarity measures based on Longest Common Subsequence Similarity (LCSS), Dynamic Time Warp (DTW). The user can build a dendrogram (phylogenetic tree) of risks and identify potential relationships, similarities and dissimilarities in risk time series dynamics. All these can be used for risk analysis and selection of time series as possible proactive key risk indicators (KRIs) based on crowdsourcing, which makes risk management technologies more easily available to small and medium – size businesses.

Examples of clustering of annual series of US banks’ operational risks and default rates by industry and the base index of the global risk factor RogovIndex©Base.

Dendrogram analysis allows for better understanding of the risks in the context, seeing the similarities of close neighbours and dissimilarities of distant ones. Bench­marking sometimes can be used to summarize information and draw conclusions about the common properties of risks with similar dynamics, identify their potential sources, and select proper KRIs for scenario generation.

For example, in Fig. 5 we can see that Internal fraud (ET1) risks could be closely related to Employment practices (ET3) and thus it is possible to prioritize risk


Fig. 5 Operational risks at US Financial Institutions, screenshot, www. rogovindex. com. Cluster­ing using Pearson correlation


treatment measures in areas of employment practice in order to manage internal fraud risks (Fig. 6).



The proposed global risk factor theory describes the frequently observed interaction of different types of risks (market, credit, operational) at different assets and in different business processes. The theory opens new prospects for risk benchmarking, analysis, detection of anomalies and hidden risks, classification of risks, particularly based on hierarchical clustering of time series using the Rogov-causality2 test. This allows the creation of new proactive risk indicators for monitoring, as well as applying the market mechanisms of operational risk optimization through diversification and hedging with the use of index derivatives.


2To avoid misinterpreting the term “Rogov-causality,” one should bear in mind that the presence of Rogov-causality does not mean the existence of a proven cause-effect relationship, but rather characterizes the temporality (the existence of prevailing succession of events in time).


All Rates (Moody’s corporate default rates)

Подпись:image327Consumer Industries (Moody’s corporate default rates)

Energy & Environment

(Moody’s corporate default ———————————————————————— (>8

Подпись: 52.25%image329rates)

Retail & Distribution

(Moody’s default rates)

FIRE (Finance, Insurance,

Real Estate) (Moody’s

corporate default rates)


Banking (Moody’s corporate _________________________________

default rates)

Rogovlndex(c) Base

Technology (Moody’s

corporate default rates)

Transportation (Moody’s _______________

corporate default rates)


Utilities (Moody’s corporate ___________

default rates)

Dates: 01/01/1982 – 01/01/2010 Converter: Value Normalize: true

Similarity function: Dynamic time warping Tolerance: 90

Method: Dynamic time warping Source: www. rogovindex. com

Fig. 6 Moody’s corporate default rates, screenshot, rogovindex. com. Clustering using DTW. One of possible dendrograms

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