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EN
Since the deterministic chaos appeared in the literature, we have observed a huge increase in interest in nonlinear dynamic systems theory among researchers, which has led to the creation of new methods of time series prediction, e.g. the largest Lyapunov exponent method and the nearest neighbor method. Real time series are usually disturbed by random noise, which can complicate the problem of forecasting of time series. Since the presence of noise in the data can significantly affect the quality of forecasts, the aim of the paper will be to evaluate the accuracy of predicting the time series filtered using the nearest neighbor method. The test will be conducted on the basis of selected financial time series.
EN
The real time series (xt) can be written in an additive form, as: xt = yt + εt, where (yt) denotes the deterministic part of the series, and (εt) the stochastic part, which is associated with the presence of random noise in the time series, representing the observational noise, system noise, or a combination thereof. The reduction of random noise allows the properties of the series (yt) to be known based on analysis of series (xt). The nearest neighbours method is derived from the theory of nonlinear dynamic systems and was developed to predict the time series, but it can also be used to reduce noise. Here the time series (yt) is built on the basis of the nearest neighbours of vectors xtm of a reconstructed state space dynamic system, which is described with the use of the time series (xt). In this paper, the nearest neighbours method is used to reduce random noise in an economic time series. Empirical studies are conducted based on actual data of an economic nature.
EN
The research on price volatility in the capital market, which have been conducted for many years led to create a wide variety of analytical approaches. One of them is developed by T. Vage coherent market hypothesis. To describe the volatility in the stock market T. Vaga proposed nonlinear statistical model based on the theory of social imitation. This model assumes transitions between different states of the capital market: from a state of effective market to a state of chaotic and coherent market. In this paper Vaga's hypothesis will be verified in the Polish capital market. Detailed research will be states of chaotic market, which will be verified by Lyapunov exponents.
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EN
Since 1975, when the R. May and J.R. Beddington informed about the possibility of application of chaos theory in economics, built many new economic models with chaotic dynamics and chaos have been identified in a number of already existing models. This paper presents briefly the theory of deterministic chaos and properties of chaotic dynamic. In addition, presents some economic models of chaotic dynamics.
PL
Od momentu pojawienia się w literaturze pojęcia deterministycznego chaosu można zaobserwować ogromny wzrost zainteresowania wielu badaczy teorią nieliniowych układów dynamicznych. Owo zainteresowanie zaowocowało pojawieniem się nowych metod predykcji szeregów czasowych, tj. metody największego wykładnika Lapunowa oraz metody najbliższych sąsiadów. Rzeczywiste szeregi czasowe są zwykle zaburzone przez szum losowy, który może komplikować problem ich prognozowania. Obecność szumu w danych może znacząco wpływać na jakość otrzymanych prognoz, dlatego głównym celem artykułu będzie ocena dokładności prognozowania szeregów czasowych poddanych procesowi redukcji szumu losowego oraz ocena efektywoności wybranej metody redukcji.
EN
Since the deterministic chaos appeared in the literature, we have observed a huge increase of interest in nonlinear dynamic systems theory among researchers. This interest has led to the creation of new methods of time series prediction, e.g. the method of the largest Lyapunov exponent and the nearest neighbors. Real time series are usually distributed by random noise, which can complicate the problem of time series forecasting. As the presence of noise in the data can significantly affect the quality of forecasts, the aim of the article is to evaluate the accuracy of predicting the time series filtered using the nearest neighbor method and the effectiveness of the chosen method of reduction.
EN
The Oseledec theorem (1968) and the theorems given in the paper Eckmann, Ruelle (1985) show the Lyapunov exponents exist for almost all the points in the state space of a dynamical system, and they are constant for almost all points in the basin of attraction of the attractor of dynamical system. However, the above-mentioned theorem applies only to deterministic systems. The Oseledec theorem provides the stability of the largest Lyapunov exponent regardless of the number of observations for the time series generated by deterministic chaotic system. While for the time series generated by a stochastic system, increase the number of observations in a series will cause change in the value of the largest Lyapunov exponent. In this paper researched the effect of the number of observations of the time series on the value of largest Lyapunov exponent. In addition, the stability of the largest Lyapunov exponent was examined in the time series after random noise reduction procedure.
EN
Real time series are usually disturbed by random noise and the presence of noise in the data can significantly affect the characteristics of dynamic system. The aim of the article will be to research the effect of re duction of random noise by the nearest neighbor method on the identification of chaos in time series. The test will be conducted on the basis of selected financial time series.
EN
In this paper has been researched the effect of random noise reduction on the accuracy of forecasts of economic time series obtained using the largest Lyapunov exponent method (LEM). The aim of the article was to compare the prediction errors obtained by LEM for the series before and after the random noice reduction and the time series filtred by models ARMA. The nearest neighbors method was used to reduce random noise in economic time series.
PL
Publikacja H. Markowitza na temat wyznaczania optymalnego portfela inwestycyjnego spowodowała ogromny wzrost zainteresowania wielu badaczy analizą portfelową. Na przestrzeni ostatnich 60 lat pojawiły się liczne modyfikacje modelu Markowitza, a także powstało wiele nowych metod i modeli. Nowym podejściem, proponowanym w poniższym opracowaniu, jest zastosowanie wykładnika Hursta do wyznaczenia składu portfela optymalnego. Celem opracowania jest konstrukcja portfela optymalnego na podstawie wykładnika Hursta, miary TMAI oraz portfel Markowitza.
EN
The publication of H. Markovitz on determining the optimal investment portfolio resulted in a huge increase of interest of many researchers of portfolio analysis. Over the past 60 years there have been numerous modifications of the Markowitz model, as well as many new methods and models. A new approach proposed in the following paper is the use of the Hurst exponent to determine the optimal portfolio composition. The paper aims to construct an optimal portfolio on the basis of the Hurst exponent, the TMAI measures and the portfolio of Markowitz.
PL
Zjawisko bezrobocia obserwuje się w sytuacji, w której ludność zdolna do pracy oraz deklarująca gotowość i chęć jej podjęcia nie znajduje zatrudnienia. Rosnący od 2009 r. poziom bezrobocia stanowi jeden z najbardziej istotnych i trudnych do rozwiązania problemów polskiej gospodarki. Wynika on między innymi z przekształceń gospodarczych, wzrastającego postępu techniczno-organizacyjnego w sferze produkcji, upadku całych gałęzi przemysłu, a także z braku odpowiednich kwalifikacji, braku doświadczenia zawodowego, niewielkiej mobilności ludności oraz wysokim kosztom dojazdu do pracy. Ze względu na długoterminowość tego zjawiska można obserwować negatywny wpływ na standard życia ludności, dynamikę rozwoju gospodarczego oraz nastroje społeczne. Celem artykułu jest ocena zagrożenia bezrobociem województw Polski w latach 2005–2012. W badaniach wykorzystano dane pochodzące z Banku Danych Lokalnych GUS-u (www.stat.gov.pl).
EN
Unemployment is observed when an individual is able to work and declares his or her readiness and willingness to take employment yet is not employed. Since 2008, rising unemployment has been one of the most important and difficult problems facing the Polish economy. On one hand, Poland’s unemployment has stemmed from economic transformation, technical and organisational progress in the sphere of production, and the collapse of entire industries. On the other, the lack of qualifications and experience, low job mobility and high commuting costs are also to blame. Due to its long-term nature, it has adversely affected the Poland’s standard of living, the dynamics of economic development and sentiments in society. The main aim of this article is to assess the threat of unemployment Poland’s voivodships faced in the years 2005–2012. The study employs a number of taxonomic measures and uses data from the Local Data Bank of the Central Statistical Office.
PL
Jednym z najbardziej istotnych narzędzi stosowanym w inwestowaniu jest analiza portfelowa. Jej głównym celem jest dywersyfikacja ryzyka inwestycyjnego. W ostatnich latach, obok klasycznej metody Markowitza, badacze rozwinęli zarówno metody będące modyfikacjami tej koncepcji, jak i stworzyli nowe, alternatywne narzędzia. Innym zaproponowanym tu podejściem jest zastosowanie miary identyfikacji chaosu polegającej na wyznaczeniu największego wykładnika Lapunowa. Celem artykułu jest konstrukcja portfela optymalnego z zastosowaniem największego wykładnika Lapunowa, miary TMAI oraz portfela Markowitza.
EN
Portfolio analysis is one of the most important techniques for investing in the capital market. Its main goal is to diversify the investment risk. In addition to the classical concept of Markowitz, researchers have developed methods which are its modifications, but they have also created new, alternative tools. An alternative approach proposed in the paper is the use of the measure for identifying chaos, i.e. the largest Lyapunov exponent. The paper aims to construct optimal portfolios determined based on the largest Lyapunov exponent, the TMAI measure and the Markowitz portfolio.
PL
Zachodzące od lat osiemdziesiątych XX wieku zmiany demograficzne w Polsce uwidoczniają wyraźny proces starzenia się społeczeństwa, na który ogromny wpływ mają: rozrodczość, umieralność i migracja. Zjawisko to jest poważnym problemem demograficznym i społeczno‑ekonomicznym, gdyż może prowadzić do wielu niekorzystnych konsekwencji, takich jak zwiększenie wydatków ze środków publicznych, zmiana zasad funkcjonowania systemów zabezpieczenia społecznego, opieki zdrowotnej i szkolnictwa, zwiększenie popytu na usługi opiekuńcze, obniżenie świadczeń emerytalno‑rentowych oraz zasiłków socjalnych, wydłużenie wieku emerytalnego, wzrost stopy bezrobocia, masowa migracja zarobkowa. W artykule przeprowadzono analizę przestrzenną potencjału demograficznego oraz poziomu bezrobocia w Polsce. W celu weryfikacji hipotezy mówiącej, że proces starzenia się społeczeństwa negatywnie wpływa na poziom stopy bezrobocia, zbadano zależność między poziomem bezrobocia a potencjałem demograficznym Polski w latach 2002, 2008 i 2014.
EN
The demographic changes occurring in Poland since the 1980s clearly show the aging of the population on which fertility, mortality and migration have a huge impact. This phenomenon is a serious demographic and socio‑economic problem because it may lead to many adverse consequences, i.e. an increase in public expenditure, policy changes regarding the functioning of social security, health and education, increased demand for care services, a decrease in pension benefits and social benefits, the elongation of the retirement age, as well as an increase in unemployment and mass migration. In the study, we will carry out a spatial analysis of the demographic potential and the level of unemployment in Poland. In order to verify the hypothesis that the aging process of socjety negatively affects the level of unemployment, the relationship between the level of unemployment and the demographic potential in Poland in 2002, 2008 and 2014 will be examined.
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