The aim of this article is to present original application wavelets to the prediction of short-term of time series. The model proposed to predict short-term time series (in particular for predicting macroeconomic indicators) is a model of copyright. The model is based on wavelet analysis, the Haar wavelet, the Daubechies wavelet and adaptive models. The Daubechies wavelets are a family of orthogonal wavelets and are characterized by a maximal number of vanishing moments for some given support. Adaptive models have been appropriately modified by the introduction of a wavelet function and combined into one predictive model. The results obtained from the study results indicate that the authorial model is an effective tool for short-term predictions. The model was applied to predict macroeconomic indicators.

The aim of this article is to present author's application of wavelets to predict short-term macroeconomic indicators.Proposed to predict short-term time series (in particular for predicting macroeconomic indicators), proprietary model is based on wavelet analysis with Haar wavelets, Daubechies wavelets, and adaptive models; they are the trend crawling model and alignment exponential model. Adaptive models have been modified through the introduction of wavelet function and combined into a single forecast model. Obtained from conducted research results, it shows the model an effective instrument to predict the short-term.

Streszczenie: Celem badania jest ocena wpływu zaproponowanej metody rozszerzenia próbki na trafność prognozy szeregów, w tym przypadku indeksu WIG. Prognozę szeregu prezentującego WIG wykonano na podstawie modelu opartego na transformacie falkowej. Przed przystąpieniem do aplikacji rozszerzenia szeregu wejściowy szereg danych podzielono na próbki o parzystej liczbie obserwacji celem wyznaczenia dokładniejszych prognoz. W artykule skoncentrowano się tylko na dodatkowym rozszerzeniu próbki przy wyznaczaniu współczynników, omijając proces predykcji. Zatem nie opisano w artykule szczegółowo modelu zastosowanego do predykcji, ponieważ nie jest celem artykułu ocena zdolności predykcyjnych modelu, a jedynie wpływ na końcowy wynik prognozy metody rozszerzenia szeregu przy wyznaczaniu współczynników k a .

The aim of this paper is to characterise the green bond market in the Visegrad Group of countries (V4) and to identify the determinants and benefits of issuing green bonds. The specific objective is a spatial–temporal analysis of the green bond yield in V4 countries. The following research methods were used in the paper: a source literature analysis and report analysis, statistical data analysis (from international financial markets), and the Dynamic Time Warping method (DTW). DTW comprises a class of algorithms that are used to compare both equal and unequal time series. The DTW method allows the smallest distance between two time series of different lengths to be found while allowing for the transformation over time of both series. As the method is highly efficient, it is used to provide a thorough spatial–temporal analysis of green bonds. The research process confirmed that green bonds are an instrument with potential in the global debt market. Among the most important stimulants for the issuance of green government bonds are capital mobilisation, the development of the green financial market, investor demand, and reputational benefits.

The aim of this paper is to analyze globalization in China in the context of comparative analysis with other countries. The analysis is based on the globalization index, which combines in one number: actual economic flows, economic restrictions, data on information flows, data on personal contact and data on cultural proximity. Trend analysis and long and short period dependencies in globalization are based on the DTW algorithm and wavelet analysis. A discrete wavelet was used for wavelet analysis of the time series studied. In the process of discrete wavelet transformation, the received signal is divided into so-called approximation and detail. The approximation is then subjected to a subsequent division into further approximation and detail, while details are not subject to further divisions. In this way, the signal is presented as the sum of the approximation of the last level and the details from all levels. The study was conducted on a group of 146 countries. In the article, globalization is understood as a process of interaction and integration among the people, companies, and governments of different nations, a process driven by international trade and investment and aided by information technology. This process has effects on the environment, culture, political systems, economic development and prosperity, and human physical well-being in societies around the world.