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Application of the Differential Evolution Algorithm to Group a Bank's Individual Clients

100%
Domański C., Kubacki R.
Argumenta Oeconomica Cracoviensia
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2020
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issue 1(22)
9-20
EN
Objective: The aim of the article is to present the results of grouping individual clients of a bank with the differential evolution algorithm. Research Design & Methods: The research offers conclusions based on analysis of the bank’s customer base and deductive and inductive reasoning. Findings: The results of the authors’ research show that the differential evolution algorithm correctly groups bank customers and can be used for this purpose. Implications/Recommendations: The differential evolution algorithm is an alternative to the commonly used k-means algorithm. The algorithm generates several competing solutions in one iteration. It enables independence from starting vectors and greater effectiveness in searching for an optimal solution. The differential evolution algorithm was itself enriched with a variable that allows the optimal number of clusters to be selected. Each iteration contained proposed solutions (chromosomes) that were evaluated by the target function built on the CS measure proposed by Chou. Contribution: The article presents the application of the differential evolution algorithm to group a bank’s clients.
2
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In Search of Hedges and Safe Havens in Global Financial Markets

100%
Wanat S., Śmiech S., Papież M.
Statistics in Transition new series
|
2016
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vol. 17
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issue 3
557-574
EN
The aim of the paper is to search for hedges and safe havens within three instrument classes: assets (represented by the S&P500 index), gold and oil prices, and dollar exchange rates. Weekly series of returns of all the instruments from the period January 1995 – June 2015 are analysed. The study is based on conditional correlations between the instruments in different market regimes obtained with the use of copula-DCC GARCH models. It is assumed that different market regimes will be identified by statistical clustering techniques; however, only conditional variances (without conditional covariances) will be taken into account. The reason for this assumption is connected with the fact that variances can be understood as market risk, and, as such, are a good indicator of market conditions. A considerable advantage of such an approach is the lack of need to determine the number of market regimes, as it is established by clustering quality measures. What is more, the methodology used in the paper makes it possible to treat the relations between instruments symmetrically. The results obtained in the study reveal that only dollar exchange rates can be treated as a (strong) hedge and a (strong) safe haven for other instruments, while gold and oil are a hedge for assets.
3
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Estimation of Population Averages on the Basis of a Vector of Cluster Means

75%
Wywiał J., Department of Statistics U. o. E.
Acta Universitatis Lodziensis. Folia Oeconomica
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2004
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vol. 175
EN
The estimation of a vector of mean values is being considered. The vector estimator consists of simple cluster sample means. It is assumod that a population of a fixed size is divided into mutually disjoint clusters each of the same size. The variance-covariance matrix of the vector estimator is derived. It is a function of a homogeneity matrix of multidimensional variable which describes within-cluster spread of the multidimensional variable under research. The accuracy of estimation is measured by means of standard deviations of particular sample cluster means as well as by means of the trace or the determinant or the maximal eigenvalue of the variance-covariance matrix of the vector estimator. The accuracy of the vector of simple sample cluster means is compared with the accuracy of the vector of the simple sample means. The accuracy of the vector of simple sample cluster means increases when the degree of within-cluster spread of the distribution of a multidimensional variable increases. Hence, the population should be divided into such clusters that the within-cluster spread is as large as possible.
PL
Zakłada się, że skończona i ustalona populacja jest podzielona na równoliczne i rozłączne grupy. Na podstawie prostej próby grupowej jest wyznaczany wektor średnich, który daje oceny wektora przeciętnych w populacji. Wyprowadzono macierz wariancji i kowariancji wektora wartości średnich z próby grupowej. Jest ona zależna od macierzy wewnątrzgrupowej jednorodności rozkładu wielowymiarowej zmiennej. Precyzja estymacji jest oceniana za pomocą wariancji poszczególnych średnich z próby grupowej, śladu, wyznacznika lub maksymalnej wartości własnej macierzy wariancji i kowariancji. Precyzja wektora średnich z próby grupowej jest porównywana z precyzją wektora średniej z próby prostej. Okazuje się, że wektor średnich z próby grupowej jest precyzyjniejszy od wektora przeciętnych z próby prostej, gdy stopień wewnątrzgrupowego zróżnicowania wartości zmiennych jest dostatecznie duży.
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