Papers by Magda Komorníková
Advances in Intelligent Systems and Computing, 2017
We propose a new method for constructing fuzzy measures. This method is based on a fixed aggregat... more We propose a new method for constructing fuzzy measures. This method is based on a fixed aggregation function A, similarity measure S and a vector \(\mathbf {x} \in [0,1]^n\). Some illustrative examples yielding parametric families of fuzzy measures are given, and some properties of our method are studied.
In this paper (which is a substantially extended version of a conference paper from SMTDA 2016 [1... more In this paper (which is a substantially extended version of a conference paper from SMTDA 2016 [10]) we focus our attention to 3-dimensional copula models of returns of indices of US financial markets (various bond indices have been investigated in the literature much less than stock indices). We have gained interesting experience in constructing Vine copula models. Although, for our particular data (comprising two triples of bond indices: US Investment Bond indices and US Corporate Bond indices), the global dominance of more traditional classes of elliptic (especially Student type) 3-dimensional copulas was demonstrated (and some conclusions concerning optimizations of investment portfolios can be based on fairly simple arguments), the optimal local Vine copulas helps to obtain more insight in the detailed development of the investigated triples of investments.
Slovak Journal of Civil Engineering, 2017
It is widely acknowledged that in the hydrological and meteorological communities, there is a con... more It is widely acknowledged that in the hydrological and meteorological communities, there is a continuing need to improve the quality of quantitative rainfall and river flow forecasts. A hybrid (combined deterministic-stochastic) modelling approach is proposed here that combines the advantages offered by modelling the system dynamics with a deterministic model and a deterministic forecasting error series with a data-driven model in parallel. Since the processes to be modelled are generally nonlinear and the model error series may exhibit nonstationarity and heteroscedasticity, GARCH-type nonlinear time series models are considered here. The fitting, forecasting and simulation performance of such models have to be explored on a case-by-case basis. The goal of this paper is to test and develop an appropriate methodology for model fitting and forecasting applicable for daily river discharge forecast error data from the GARCH family of time series models. We concentrated on verifying whe...
Asterisque- Societe Mathematique de France
Mathematica Slovaca, 1981
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz
Mathematica Slovaca
Katedгa kybemetiky SVŠT Gottwaldovo nám. 19 812 43 Bratislava Katedra teórie pravdepodobnosti a m... more Katedгa kybemetiky SVŠT Gottwaldovo nám. 19 812 43 Bratislava Katedra teórie pravdepodobnosti a matematickej štatistiky Matematicko-fyzikálnej fakulty UK Mlynská dolina 842 15 Bratislava
New Trends in Aggregation Theory, 2019
We analyzed quarterly seasonally-filtered time series (OECD link) of GDP in EURO per capita for t... more We analyzed quarterly seasonally-filtered time series (OECD link) of GDP in EURO per capita for the V4 countries (Visegrad treaty - Czech republic, Hungary, Poland, Slovakia) and Germany in the period 1996/Q1 – 2018/Q1. First, ARIMA models were used to clear the temporal dependence, then marginal distribution functions were utilized to standardize the data such that it is U(0,1) distributed. Dependence among the 5 random variables was analyzed in terms of correlation strength and joint distribution modeled by elliptical, vine and factor copulas, both in the whole 22 years period and 6-year rolling windows with 3-year overlaps. The choice of such different model classes allows us study the nature of underlying dependence structure from different standpoints.
Tatra Mountains Mathematical Publications, 2017
Stock and bond markets co-movements have been studied by many researchers. The object of our inve... more Stock and bond markets co-movements have been studied by many researchers. The object of our investigation is the development of three U.S. investment grade corporate bond indices. We concluded that the optimal 3D as well as partial pairwise 2D models are in the Student class with 2 degrees of freedom (and thus very heavy tails) and exhibit very high values of tail dependence coefficients. Hence the considered bond indices do not represent suitable components of a well-diversified investment portfolio. On the other hand, they could make good candidates for underlying assets of derivative instruments.
Journal of Statistical Theory and Applications, 2016
In this paper, we extend our investigations of a special class of perturbations of copulas introd... more In this paper, we extend our investigations of a special class of perturbations of copulas introduced in [7]. Despite a surprising fact that this kind of perturbations does not change the value of tail dependence of the original copulas, their use yielded models with considerably improved fitting qualities.
Data Analysis and Applications 2
summary:The autocorrelation function describing the linear dependence is not suitable for descrip... more summary:The autocorrelation function describing the linear dependence is not suitable for description of residual dependence of the regime-switching models. In this contribution, inspired by Rakonczai ([20]), we will model the residual dependence of the regime-switching models (SETAR, LSTAR and ESTAR) with the autocopulas (Archimedean, EV and their convex combinations) and construct improved quality models for the original real time series
Deterministic and stochastic approach to modeling common trends has been applied to time series o... more Deterministic and stochastic approach to modeling common trends has been applied to time series of horizontal coordinates of the permanent GPS station Modra-Piesky (recorded weekly during the period of 4 years). 1. ONE DIMENSIONAL ANALYSIS OF COORDINATE DATA The U.S. Global Positioning System (GPS) is the satellite navigation system applied in geodesy for precise determination of the position on the Earth's surface. GPS is used for the regular monitoring of recent kinematics of the Earth's crust. The daily geocentric Cartesian coordinates of about 80 permanent GPS stations are deter-mined within the framework of the European GPS network EUREF (see [4]). One site in Slovakia is participating in this project- the Modra-Piesky (MOPI) per-manent observation station. The MOPI station has been operating regularly since June, 1996 (see [6]). In this paper we analyze a series transformed to a horizon-tal coordinate system covering the interval from November 1996 to October 2000. T...
Acta Hydrologica Slovaca, 2019
Analýza hydrometeorologických časových radov predstavuje dôležitú súčasť posudzovania zmien hydro... more Analýza hydrometeorologických časových radov predstavuje dôležitú súčasť posudzovania zmien hydrologických procesov. Pochopenie zmien časových radov prináša lepšie pochopenie príčin týchto zmien. Časové rady údajov je možné podrobiť veľkému množstvu analýz, jednými z nich je aplikácia štatistických metód. Tento článok sa zaoberá analýzou vnútornej štruktúry a zmien priemerných mesačných, ročných a sezónnych prietokov vo vybraných vodomerných staniciach na Slovensku pomocou základnej popisnej štatistiky, trendovej analýzy, analýzy periodickej zložky, AR-ARCH modelu a viacrozmernej analýzy. Uvedené metódy boli aplikované na piatich väčších povodiach v rámci Slovenska a siedmich menších povodiach nachádzajúcich sa v severnej časti povodia Váhu. Výsledky poukazujú na najväčšie zmeny (v trendovej a periodickej zložke) na toku Hron. Z menších povodí, najmä toky Kysuca a Bystrica vykazujú štatisticky významne klesajúce trendy. KĽÚČOVÉ SLOVÁ: štatistické metódy, priemerné mesačné prietoky, trendová analýza, AR-ARCH model THE CHANGE ANALYSIS OF THE MEAN MONTHLY DISCHARGES IN SLOVAKIA IN RECENT DECADES. An analysis of a hydrometeorological time data series is an important part in assessing changes in hydrological processes. Understanding changes in time series results in a better understanding of the causes of these changes. A time data series can be evaluated by a large number of analyses. One of them is the application of statistical methods. The article deals with a basic analysis of the mean monthly, annual, and seasonal discharges in selected stagedischarge gauging stations in Slovakia using statistical methods. The time data series were subjected to basic descriptive statistic, trend and periodicity analyses, and AR-ARCH model. These methods were applied to five larger basins in Slovakia and seven smaller basins located in the northern part of the Váh River basin. The results show greatest changes (in trend and periodic analysis) in the Hron River. From the smaller river basins, especially Kysuca and Bystrica River, there are statistically significant decreasing trends.
Economic Modelling, 2016
This paper investigates the role of gold as a safe haven in international stock markets using var... more This paper investigates the role of gold as a safe haven in international stock markets using various copula techniques to capture complex dependencies between stock markets and gold prices. It creates a new class of mix copulas from Clayton, Frank, Gumbel and Joe copulas. The paper employs parametric and nonparametric copulas to over 11years of daily data (1999–2010) from seven countries' to understand the nexus between international stock markets and gold prices. The results show that gold may be a safe haven asset during market crash for the case of Malaysia, Singapore, Thailand, the UK and the US markets but not for the Indonesian, Japanese and the Philippines markets. These results are of great interest for the investors and risk managers to comprehend portfolio diversification benefits and risk reductions during tranquil and downturn periods by including gold in their investment portfolios.
Fuzzy Sets and Systems, 2017
In this paper (which is a substantially extended version of a conference paper from AGOP 2015 [10... more In this paper (which is a substantially extended version of a conference paper from AGOP 2015 [10]), we investigate the effects of specific class of perturbations of bivariate copulas on several measures of dependence (Spearman's rho, Blomqvist's beta, Gini's gamma, Kendall's tau), and tail dependence along both diagonal sections. It is demonstrated that the influence of the perturbation parameter on the values of the first three of the above coefficients of dependence is linear, while on the last one it is quadratic. Interesting numerical analyses for several important classes of Archimedean copulas are presented. It is also demonstrated that the considered perturbations do not change the coefficients of tail dependencies along the main diagonal but linearly reduce their values along the second diagonal. An interesting possible application for analyzing dependencies along the second diagonal of copulas represent insurance data, where censoring introduces a negative dependence between the investigated components of the claims. As a by-product, we present a new class of perturbations of copulas that linearly reduce the more popular coefficients of tail dependencies along the main diagonal, while preserving their values along the second diagonal. Subsequently using suitable elements of both above classes of perturbations, any original copula can be transformed to a resulting one, having coefficients of tail dependencies along both diagonals linearly reduced (with any couple of preselected linear proportions from [0, 1]).
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Papers by Magda Komorníková