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Miltivariate measures of dependence based on copulas

100%
Heilpern S.
Mathematical Economics
|
2014
|
issue 10(17)
17-32
EN
The paper is devoted to the multivariate measures of dependence. In contrast to the classical approach, where the pairs of variables are studied, we investigate the dependence of more than two variables. We mainly consider the measures based on copulas. These are the multivariable generalizations of the known coefficients of such correlation as Spearman’s rho, Kendall’s tau, Blomquist’s beta and Gini’s gamma. We present the definitions, the constructions and the basic properties of such multivariate measures of dependence. The case of large number of dimension, greater than two, presents more complications. We have several different versions of such generalization in this case and the lower bound of the values of such measures of dependence are close to zero. We also study the multivariate tail dependences. The last part of the paper is devoted to the estimation of multivariable versions of Spearman’s rho coefficient.
2
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Price duration versus trading volume in high-frequency data for selected DAX companies

100%
Gurgul H., Robert S., Mitterer C.
Managerial Economics
|
2016
|
vol. 17
|
issue 2
241-260
EN
The main goal of this paper is to gain insights into the dependence structure between the duration and trading volume of selected stocks listed on the Frankfurt Stock Exchange. We demonstrate the usefulness of the copula function to describe the dependence of specific unevenly spaced time series. The properties of the time series of price durations and trading volumes under study are in line with common observations from other empirical studies. We observe clustering, overdispersion, and diurnality. For most of the stocks, the seminal model (linear parametrization with exponential or Weibull distribution) can be replaced by a logarithmic specification with more-flexible conditional distributions. The price duration and trading volume associated with this duration exhibit dependence in the tails of distribution. We may conclude that high cumulative trading volumes are associated with long duration. However, changes of price over short times are related to low cumulative volume.
3
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The testing of causal stock returns-trading volume dependencies with the aid of copulas

88%
Gurgul H., Mestel R., Syrek R.
Managerial Economics
|
2013
|
vol. 13
21-44
EN
This paper is concerned with a dependence analysis of returns, return volatility and trading volume for five companies listed on the Vienna Stock Exchange. Taking into account the high frequency data for these companies, tests based on a comparison of Bernstein copula densities using the Hellinger distance were conducted. It is worth noting that these tests can be used in general settings since there is no restrietion on the dimension of the data. The parameter which must be set up for the testing procedure is a bandwidth. It is necessary for estimation of the nonparametric copula. The paper presents some patterns of causal relationships between stock returns, realized volatility and expected and unexpected trading volume. There is linear causality running from realized volatility to expected trading volume, and a lack of nonlinear dependence in the opposite direction. The authors detected strong linear and nonlinear causality from stock returns to expected trading volume. Therefore, a knowledge of past stock returns can improve forecasts of expected trading volume. They did not find causality running in the opposite direction.
4
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The structure of contemporaneous price-volume relationships in financial markets.

88%
Gurgul H., Syrek R.
Managerial Economics
|
2013
|
vol. 14
39-60
EN
The main goal of this paper is an examination of the interdependence stuctures of stock returns, volatility and trading volumes of companies listed on the CAC40 and FTSE100. The authors establish that the mean values of respective measures are different on the markets under study. In general, they are larger for equities from CAC40 than from FTSE100. The Mixture of Distributions Hypothesis with long memory is rejected for about 70 % of stocks from both markets. Additionally fractional cointegration was tested. The lack of fractional cointegration, suggests a rejection of the last variant of MDH in all cases, i.e. the time series under study do not exhibit common long-run dependence. The analyzed time series are not driven by a common information arrival process with long memory. Correlation between volatility and trading volume is present for all the stocks of companies from these markets. The mixtures of rotated copulas and Kendall correlation coefficient allowed the checking of extreme return-volume dependence structures. The empirical results reflect significant dependencies between high volatility and high trading volume. In general, the dependence structures of stock returns and trading volume are different. In the case of CAC40 companies high trading volume is not correlated as frequently with high stock returns as with low stock returns. For companies listed on the FTSE100 high stock returns are mostly related with high trading volume.
5
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Zastosowanie kopuli w zadaniu minimalizacji wartości zagrożonej portfela

75%
Lach A.
Optimum. Studia Ekonomiczne
|
2015
|
vol. 2(74)
PL
W artykule zastosowano wybrane kopule w zadaniu minimalizacji wartości zagrożonej (VaR) portfeli w okresach charakteryzujących się odmiennym typem trendu. Rozkłady empiryczne stóp zwrotu z akcji 10 spółek wchodzących w skład indeksu WIG20 połączono kopulami Gaussa, t-Studenta, Claytona, Franka, Gumbela i odwróconą Gumbela. Symulacje z tak otrzymanych rozkładów wielowymiarowych stanowiły podstawę do utworzenia portfeli minimalizujących wartość zagrożoną. Jakość VaR, wyliczoną dla pozycji krótkiej i długiej, oceniono testem Kupca. Wartość zagrożona została poprawnie wyznaczoną dla rozkładów utworzonych za pomocą: dwóch kopuli archimedesowych uwzględniających zależność w dolnym ogonie (Claytona i odwróconej Gumbela), jednej kopuli z symetryczną zależnością w ogonach (t-Studenta) oraz jednej kopuli nie mającej zależności w ogonach (Gaussa).
EN
In the paper, selected copulas are applied in the task of minimizing the value at risk (VaR) of portfolios in the periods characterized by different types of trend. Empirical distributions of returns on 10 companies listed on WIG20 index are combined with Gaussian, t-Student, Clayton, Frank, Gumbel, and rotated Gumbel copulas. Simulations from thus obtained multivariate distributions are the basis for minimizing the VaR of portfolios. The quality of the VaR, calculated for both short and long positions, are assessed with the Kupiec test. The value at risk is properly set for joint distributions created with the following copulas: two Archimedean copulas with lower tail dependence (Clayton and rotated Gumbel), one copula with symmetric dependence in tails (t-Student), and one copula with no tail dependence (Gaussian).
6
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Status gramatyczny predykatywnych SZKODA , WSTYD , ŻAL raz jeszcze

71%
Przepiórkowski A.
Polonica
|
2019
|
vol. 39
85-110
EN
The apparently nominal forms szkoda ‘pity’, wstyd ‘shame’, żal ‘regret’, when used predicatively, have been analysed either as ‘quasi-verbs’ (inflecting only for tense and mood), or as adverbs, or as nouns. The author recalls and reinforces arguments against their verbal analysis, and shows that such forms are categorially ambiguous. In their adverbial guise, they may be modified by other adverbs, they do not agree with the copula, they may co-occur with a dative experiencer, and they may occur in other predicative constructions, apart from copular constructions. In their nominal guise, they may be modified by adjectives, they agree with the copula, they do not easily combine with a dative experiencer, and they do not occur in other predicative constructions. The author also argues that this categorial ambiguity is correlated with the two copular constructions in Polish: one involving the purely verbal copula być ‘be’ and the other involving the so-called ‘pronominal’ copula to (być).
PL
Pierwszym celem niniejszego artykułu jest potwierdzenie, że predykatywne szkoda, wstyd, żal nie są czasownikami niewłaściwymi. Dwa inne poglądy na temat statusu jednostek typu szkoda mówią, że są to przysłówki lub rzeczowniki. Autor pokazuje, że oba są prawdziwe: omawiane jednostki są kategorialnie niejednoznaczne, przy czym istnieje szereg testów pozwalających odróżnić użycia adwerbialne od użyć nominalnych. Przedstawia także argumenty za tym, że kategoria gramatyczna predykatywnych użyć omawianych jednostek skorelowana jest z typem konstrukcji łącznikowej, w której występują: formy przysłówkowe z łącznikiem być, natomiast formy rzeczownikowe – z łącznikiem to.
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