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PL
W pracy przedstawiono dwa podejścia, służące do badania dynamicznej zależności pomiędzy finansowymi szeregami czasowymi. W pierwszym podejściu do badania zależności między szeregami czasowymi wykorzystano funkcje kopuli oraz dynamikę sterowaną ukrytym procesem Markowa, natomiast drugie podejście wykorzystuje wielowymiarowe procesy auto-regresyjne. W wyniku zastosowania obu podejść otrzymano dynamiczne korelacje pomiędzy badanymi szeregami czasowymi, które stanowiły podstawę do konstrukcji dynamicznego grupowania rynków finansowych.(abstrakt oryginalny)
EN
In the paper, authors present the analysis of the relative occupation time. The ana- lysis concerns the mean of relative occupatio n time determined on the basis of the stock price taken from the first and second half of the day. The presented analysis does not exhaust the family of possible applica tions of occupation time functional.
XX
The authors of this paper present the architecture of a multi-agent system which supports investment decisions on the stock market. The individual components of the system, the manner of communication between them, the mechanism of assessing the individual agents are discussed. New methods of pre-processing financial series, the concept of never-ending learning, the behavioural model of stock exchange traders and the manners of translating the modelled patterns into the open and close position signals are described. The results of the research are described and the directions of the further development of the platform are provided in the conclusion.
PL
Filtracja danych jest bardzo ważnym etapem badań związanych z odróżnianiem szeregów chaotycznych od losowych. Jedną z metod wykorzystywanych w tym celu jest metoda najbliższych sąsiadów. Pierwotnie została ona stworzona w celu prognozowania, jednak późniejsze prace badawcze pokazały, że jest ona również dobrym narzędziem umożliwiającym redukcję szumu w szeregach czasowych. Celem artykułu jest zbadanie wpływu redukcji szumu metodą najbliższych sąsiadów na identyfikację chaosu w wybranych szeregach czasowych. Badanie będzie przeprowadzone na podstawie ekonomicznych szeregów czasowych, złożonych z cen zamknięcia akcji spółek notowanych na GPW w Warszawie oraz dziennych kursów walut.
EN
The data filtration is very important stage of research involving distinguishing the chaotic series from random series. One of the methods used for this purpose is the nearest neighbor method. It was originally designed to predict, but later research showed that it was also a good tool for reducing noise in the time series. The aim of the article will be to study the effect of noise reduction, carried out using the nearest neighbor method, on the identification of chaotic dynamics in the selected time series. The test will be conducted based on the economic time series which consist of closing prices of companies listed on the Warsaw Stock Exchange and the daily exchange rates.
EN
In the paper the problem of prediction of a time series is considered. Time series observations can be measured on order scale. On the basis of observed ranks of values of the variables observed in the past periods a forecast of the rank of the observation in the future period is determined. The proposed method results from the derivation of the distribution of the well known Kendall's rank coefficient. The paper was inspired by a lecture of Jean H.P. Paelinck who gave it at the University of Economics in Katowice when he received the title of doctor honoris causa of the University in 1987.
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
The goal of this article was to investigate the correlations between futures prices of commodities quoted on the CME. The sample includes corn, soybeans and wheat. Using ARIMA model for which best parameterization was identified based upon the AIC value, the raw time series of the prices for the contract with the shortest time left to expiration were subject to the process of removing a stochastic trend as well as autocorrelation. The transformed time series were then used as an input in fitting various theoretical distributions whose practical importance in describing the process of prices had been proven in the literature. The unknown parameters were estimated by means of the ML. Three different tests, namely χ2, Kolomogorov and AD, were employed in order to investigate/ verify the goodness-of-fit of these distributions. Finally, the parameters of normal as well as t copulas were estimated by means of the two-step ML method, with different hypotheses concerning the form of a correlation matrix. The goodness-of-fit test based on Cramer-Mises statistic was used to choose between the alternative copulas, with the critical values being obtained via non-parametric boostrap.
PL
W pracy została przeprowadzona charakterystyka szeregów cen energii elektrycznej pod względem obserwacji, odstających na Polskiej Towarowej Giełdzie Energii (TGE). Do analizy zostały wykorzystane szeregi czasowe o dziennej częstotliwości indeksów IRDN, SIRDN, offIRDN, POLPXbase oraz POLPXpeak. Na podstawie wyników estymacji modelu ARIMA zostały zidentyfikowane obserwacje odstające: addytywne (AO), innowacyjne (IO), przesunięcie poziomu (LS) oraz tymczasowe zmiany (TC).
EN
In the paper outlier observations within time series of prices of electric energy from Polish Power Exchange were characterized. Time series of indexes IRDN, sIRDN, offIRDN, POLPXbase and POLPXpeak with daily frequency were analyzed. Additive outliers (AO), innovative outliers (IO), level shifts (LS), temporary change (TC) were identified using seasonal linear models SARIMA.
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
The aim of his article is to use the Hölder function to analysis spatial data. We show the method of generate spatial data with Hölder exponents. The article consists of two parts: the first one presents elements of analysis the Hölder function, and the second consist results of analysis in spatial dimension.
PL
W artykule uwzględniono różne podejścia do zagadnienia identyfikacji obserwacji oddalonych: podejście dedykowane dla szeregów czasowych i modeli ARIMA, mierniki stopnia oddalenia obserwacji oraz metody klasyfikacyjne. Celem cząstkowym jest zestawienie istniejących metod, ze wskazaniem możliwości pewnych modyfikacji dla polepszenia wyników otrzymywanych z prowadzonej diagnostyki.
EN
The paper presents three different methods for detecting anomalies in time series. The first one is dedicated for time series analysis and ARIMA models. Two other two come from very different background: one is associated with measuring the distance from the given observation to the remaining objects in dataset. The other one belongs to the family of classification methods within machine learning framework. The goal of the paper is to present, compare and illustrate these three different approaches on a real world dataset.
EN
The aim of the papers is to study the effect of noise reduction, carried out using the nearest neighbor method, on the identification of chaotic dynamics in the selected time series. The tools used to distinguish chaotic time series from random ones will be the BDS statistic and the correlation dimension The test will be conducted based on the economic time series which consist of closing share prices of companies listed on the Warsaw Stock Exchange and the daily exchange rates.
PL
Zaprezentowano wyniki badań przeprowadzonych przez autorów nad przydatnością różnych najnowszych modeli giełdowych do opisu danych dla spółek wziętych z giełdy szwajcarskiej (z indeksami SMI). Omówiono modele GARCH oraz modele tej klasy uwzględniające asymetrię danych. Autorzy zauważają, że decydującym kryterium dopasowania modelu do danych giełdowych jest ich skośność czyli asymetria.
EN
The aim of the paper is to prove the use of some type of GARCH models in application to 18 companies listed in SMI which is the main index of Swiss Stock Exchange. The authors concentrate on seven extensions of the APARCH model formulated by Ding, Engle and Granger in 1993 and other GARCH type models. The APARCH model couples the flexibility of a varying with the asymmetry coefficient (to take the "leverage effect" into account). Based on the AIC and RMSE criterions goodness of fitting the authors established that the most frequently the T ARCH models has been indicated as the most suitable model for returns of Swiss companies (12 cases out of 18). The next positions in this ranking occupy EGARCH and GARCH models (in each case 3 models out of 18). These results underline importance of taking into account the asymmetry of the distribution of returns. (original abstract)
PL
Celem niniejszej pracy jest wykazanie, że metody ekonometryczne oparte na teorii chaosu mogą zostać wykorzystane do opisu struktury wypłat z bankomatów. Uzyskanie potwierdzenia fraktalnych właściwości szeregów czasowych dobowych wypłat z bankomatów stworzyłoby możliwość zastosowania teorii chaosu do usprawnienia zarządzania ich siecią. W szczególności mogłoby to pomóc w doborze metod prognostycznych jakie należałoby zastosować do krótkoterminowej predykcji wypłat z bankomatów. Dodatkowo w pracy zostanie sprawdzone czy szeregi czasowe generowane przez bankomaty znajdujące się w różnych lokalizacjach różnią się co do badanych właściwości. W Polsce, zgodnie z wiedzą autorów, nie były dotąd badane właściwości chaotyczne wypłat z bankomatów. W następnym rozdziale zostanie omówiona literatura ekonometryczna dotycząca tej tematyki. W rozdziale 2 zostaną przedstawione źródła i charakterystyki opisowe danych. Rozdział 3 zawiera przegląd i opis stosowanych w pracy metod identyfikacji chaosu deterministycznego. W rozdziale 4 zostaną przedstawione wyniki uzyskanych analiz wraz z ich interpretacją. Wnioski z przeprowadzonych badań zostaną sformułowane w rozdziale 5.(fragment tekstu)
EN
Empirical results based on ATMs' withdrawals suggest existence of nonlinear structures in analysed time series. Large values of Hurst exponent are in favour of existence of long memory in time series under study and therefore confirm nonlinearity. In addition, existence of chaos is supported by convergence of correlation dimension (in all cases under study) as dimension of submersion changes. The frontier values of correlation dimension do not suggest low dimensional chaos. They suggest existence of multifractals in analysed data. However, although the largest Lyapunov exponents are positive numbers it cannot be claimed that ATMs' withdrawals exhibit surely chaotic structures, because these computed values are rather small. This fact is against fractal nature of withdrawals time series. The data with respect to deterministic chaos exhibit similar features independently of location of ATM and size of withdrawals. In future research the larger sample also from other Polish provinces should be taken into account in order to make our results more conclusive and robust. The confirmation of chaotic behavior of ATMs' withdrawals time series would justify potential application of chaos theory in management of ATMs' network, especially would allow building and estimation of forecast models.(original abstract)
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PL
Celem artykułu jest porównanie jakości prognoz zarówno ex post, jak i ex ante dotyczących zapotrzebowania na gotówkę w bankomatach, przy wykorzystaniu różnych metod prognozowania na podstawie szeregów czasowych wypłat. (fragment tekstu)
EN
The authors explain links between strategy of replenishment of ATMs and costs of ATMs holders. Cost minimalization depends on accuracy of forecasts of withdrawals from ATMs. In the paper the several forecasting methods of withdrawals from ATMs in Euronet network installed in Małopolskie and Podkarpackie voivodships are applied. The used forecasting models are compared based on quality of ex post and ex ante forecasts. The model used in forecasting process depends on many factors e.g. location of ATM or calendar effects. The importance and role of these factors are analyzed in the paper. The authors supplied evidence, that suggested forecasts based on weighted averages are more accurate than forecasts based on methods applied by other authors. (original abstract)
XX
W opracowaniu przedstawiono zastosowania adaptacyjnych metod prognozowania w predykcji krótkookresowej zjawisk o nieregularnym przebiegu w czasie. Omawiamy wyniki prognozowania, posługując się przykładem targowiskowych cen prosiąt, ponadto dokonano analizy efektywności wygładzania szeregu czasowego przy zastosowaniu wspomnianych metod. (fragment tekstu)
EN
The analysis of investment risk is strongly associated with the knowledge of dependency structure between assets. The aim of this paper is to present some dependency and concordance measures between random variables. Such measures as Pearson coefficient of correlation, Kendall's tau and Spearman's rho has been discussed. Moreover, the measures of tail dependencies has been presented. An empirical analysis has been carried out using selected assets from non-ferrous metals market.
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.
EN
The paper focuses on the sectoral disparities of the link between changes in labour productivity and employment changes. It presents tendencies and features of the labour productivity dynamics in three sectors of the polish economy. Labour productivity is one of the type of productivity which is mostly used for evaluating economic performance. Labour productivity growth is computed as gross valued added at constant prices divided by thousands of hours worked (in terms of the number of employees in total economy).
EN
In this paper two approaches to financial time series forecasting using neural networks were compared. First one, the function approximation approach, in which neural networks are trained to forecast the exact one day ahead value of stock price. And the second one, classification approach, in which the output variable is the direction of future stock price movements. The aim of this work was to check if using the classification models can lead to better results in terms of direction of change forecasting and profits generated by their forecasts. This research was conducted on the basis of the time series of daily closing stock prices for three companies listed on the Warsaw Stock Exchange. Simulations show that some of the approximating models achieved satisfactory results in terms of the directional symmetry measure, although the best results for each of the analyzed company have been achieved for classification models.
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