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The paper deals with designing a mask suitable for a selective filtering of data. The design of the mask is performed in the time-frequency domain and the selection is based on the co-movement measure of time series. We propose two approaches for the mask construction: i) hard thresholding based on χ 2 testing; ii) adaptive based thresholding. The proposed mask can be used for time series filtering in which we obtain either the adjusted time series or the construction of the time series containing only the co-moved parts. Further, after computing an inverse transform we can obtain time series with/without the co-moved area applicable for consequent econometric analyses. The paper provides recommendations concerning the selection of a particular approach in a given situation. The proposed methodology is demonstrated on the adjustment of industrial production index of Euro Area and selected G8 countries about co-movement with the US.

The paper deals with the identification of time-frequency regions describing cyclicality of bank loans before, during and after the 2008 crisis via wavelets. We bring new methods and findings about the short and medium cycles of loans provided to corporates and households in the Euro Area in 2000–2017 using seasonally unadjusted monthly data. We have recognized an impact of the crisis on data volatility which further influences the type of significance testing of wavelet spectrograms. To avoid this influence we propose: (1) an adaptive spectrogram testing based on Torrence and Compo approach and (2) robustness analysis via enhanced spectrogram modelling tested by the MC simulations. Both cross-checked approaches prove the sensitivity of standard wavelet tests on data volatility. The results confirm the usability of the new approaches and show that the crisis in 2008 influenced the cyclical behaviour of both categories of economic sectors, but in a different way.

The paper deals with the identification and the description of the co-movement between the US and G8 countries with regard to the impact of the structural change, i.e. the financial crisis in 2008. For the identification of the co-movement, we use an optimized segmentation-adaptive-based approach (SAB) of significance testing of the power wavelet cross-spectrum. The SAB testing is based on the standard testing for the power wavelet cross-spectrum adapted for the case if the data have several levels of volatility during the time evolution, i.e. the data can be split into several segments with different volatility. The number of segments is set by the heteroscedasticity test and the test for comparing variances in the segments of the time series. The SAB testing allows us to identify significant co-movement with respect to the local variance, which can reveal additional significant co-movement areas. We apply this approach to the monthly data of industrial production index for G8 countries in 1993–2017.

The paper deals with significance testing of time series co-movement measured via time-frequency approach. We use the wavelet analysis for estimation of the co/cross-spectra for the co-movement analysis. This technique is very popular in the most of economic applications for its better time resolution compare to other techniques. Such approach put in evidence the existence of both long-run and short-run co-movement. In order to have better predictive power it is suitable to support and validate obtained results via some testing approach. We investigate the test of wavelet power co/cross-spectrum with respect to the Gaussian white noise background with the use of the Bessel function. Our experiment is performed on synthetic signal and real data. We use seasonally adjusted quarterly data of gross domestic product of the United Kingdom, Korea and G7 countries. To validate the test results we perform Monte Carlo simulation. We describe the advantages and disadvantages of both approaches and formulate recommendations for using time-frequency testing for wavelet co/cross-spectra. Článek se zabývá testováním významnosti společného pohybu časových řad měřených časově-frekvenčním přístupem.

Kernel smoothers belong to the most popular nonparametric functional estimates. They provide a simple way of finding structure in data. Kernel smoothing can be very well applied on the regression model. In the context of kernel estimates of a regression function, the choice of a kernel from the different points o view can be investigated. The main idea of this paper is to present construction of the optimal kernel and edge optimal kernel by means of the Gegenbauer and Legendre polynomial.

We investigate the impact of the financial crisis on the access of small and medium-sized enterprises in the Czech Republic to external financing. We apply the non-parametric kernel density estimation on a firm-level measure of financing constraints and evaluate its distribution on a balanced panel of SMEs. We focus on financing constraints related to financial health of companies since they determine the commercial banks' lending behaviour. Our results reveal that firms were more constrained during the crisis and their financing constraints did not largely improve after the end of financial crisis. We argue that enterprises were financially constrained during the crisis because of reduced cash-flow and cash holdings. Článek zkoumá dopad finanční krize na malé a střední podniky v České republice a na externí financování. Analýza je provedena prostřednictvím neparametrického jádrového odhadu hustoty. Výsledky ukazují, že firmy byly více omezeny v průběhu krize a jejich omezení financování se příliš nezlepšilo ani skončení finanční krize.

We compare three filters commonly used for business cycle analysis: the Baxter-King, the Christiano-Fitzgerald and the Hamming window filter. Empirical contribution of the paper is numerical evaluation of the approximation of the ideal band-pass filters in the discussion of the filters theoretical properties (gain and attenuation within the business cycle frequencies, as well as the leakage in the remaining frequencies). We consider the truncation factor for the Baxter-King filter and the sample size for the latter two. We show that the leakage and attenuation of the Christiano-Fitzgerald and the Hamming window filter perform similarly across the range of chosen sample sizes and better than the Baxter-King filter. Moreover, we apply the filters to data of selected EU countries and point out differences in their estimation of growth business cycles. Our findings indicate that Christiano-Fitzgerald filter and the Hamming window both are appropriate for the identification of a business cycle. The Hamming window filter introduces smaller attenuation near the edges but in case of small samples its approximation of ideal filter is very rough. Předkládaný článek porovnává tři nejpoužívanější typy filtrů pro analýzu hospodářských cyklů, a to Baxterův-Kingův, Christianův-Fitzgeraldův filtr a filtr typu Hammingovo okno. Empirický přínos publikace je v numerickém ohodnocení aproximace ideálního pásmového filtru na základě zisku, propouštění a zdůraznění frekvenčních složek filtru. Aplikace je provedena na vybrané země EU.

Presented paper deals with comparison of chosen methods used for the business cycle identification. With respect to this aim nonparametric method (kernel smoothing) and Box-Jenkins methodology were used. This comparison is performed by application on economic activity in USA 1960/Q01–2007/Q01. The residuals are tested by Box-Pierce test. Identified trend is discussed with chosen historical events which affect business cycle in the USA.

Předkladaný přispěvek se zabýva identifikaci faktorů ovlivňujicich vývoj klesajici porodnosti v Ceske republice v obdobi 1991-2005 s přihlednutim k financni situaci a životni urovni rodin.Nejprve je provedena strucna trendova analýza složky celkove porodnosti - živě narozeni. Živě narozeni jsou dale děleni podle rodinneho stavu matky v době porodu. Je modelovan trend vývoje narozených v manželstvi a mimo manželstvi. Nasledna analýza se zabýva klesajici složkou, a to poctem narozených v manželstvi.Dale je využito korelacni analýzy ke zkoumani vlivu vybraných demografických a ekonomických velicin na vývoj klesajici složky porodnosti. Nasledně stanoveni statisticky významných nezavislých proměnných pro regresni model definujici jeji vývoj.Pote je provedena formulace vicerozměrneho regresniho modelu popisujiciho zavislost porodnosti v manželstvi na vybraných faktorech a jeho odhad. Vzhledem k rozsahlosti problemu a omezene dostupnosti potřebných dat, kdy neni možne obsahnout celou problematiku, je prace zaměřena pouze na vybrane otazky s problemem souvisejicich.

Předkladaný přispěvek se zabýva posouzenim periodicity růstoveho hospodařskeho cyklu CR v obdobi 1996/Q1 - 2008/Q4 na zakladě numericky vycislených kritických hodnot pro testovani významnosti hodnot periodogramu R. A. Fisherova testu. Zjistěne výsledky jsou porovnavany s rozdělenim cyklů dle periodicity, jak je uvaději Schumpeter (1939), Czesaný (2006) nebo Burda, Wyplozs (2001). Pro nalezeni růstoveho cyklu je využito detrendovani Hodrick-Prescottovým a Baxter-Kingovým filtrem. Dale je provedena analýza a testovani periodicity prostřednictvim periodogramu. Za timto ucelem je využito vlastniho odvozeni a numerickeho vycisleni kritických hodnot pro tento test pro 1%, 5% a 10% riziko.Na zakladě výsledků empiricke analýzy zjisťujeme, že v průmyslove výrobě můžeme najit cykly v delce trvani od 9 let nejdelsiho cyklu, přes cykly v trvani 6 let, cykly s delkou okolo 4 a 3 let, ale i kratke cykly okolo 2 let. Porovnanim zjistěných udajů se studii Schumpetera (1939) nebo Burdy, Wyplozse (2001) se lze domnivat, že průmyslova výroba Ceske republiky je z hlediska cyklickeho vývoje indikovana pohybem zasob. Připustime-li existenci dlouhodobých cyklů, pak jsou jeho zdrojem pravděpodobně dlouhodobe investice do strojů, zařizeni a technologii. Při porovnani s empirickou studii Czesaneho (2006), založenou na ekonomicke analýzy jednotlivých ukazatelů vývoje ekonomiky, dospivame ke shodě v identifikaci tzv. Kitchinových cyklů o delce 3-5 let.

Presented paper is focused on evaluation of cyclical behaviour of industrial production of the Czech Republic in time and frequency domain. Analyses in both domains are done in the context of commonly used detrending techniques necessary for obtaining growth business cycle. In the case of time domain analysis, the length of existing cycles is calculated on the basis of dating method application, i.e. right and left version of naive rules as well as Bry–Boschan algorithm. In the case of frequency domain, estimate of the spectra using periodogram and autoregressive process with optimum lag are used. In the time domain evaluation of the unity of the results of detrending techniques from the turning points identification is done as well. All analysis are done on the data of industrial production in the Czech Republic in 1996/Q1–2008/Q4.

We employ a wavelet spectrum analysis to study globalization and business cycles in China and G7 countries. The co-movement synchronization between G7 countries and China is shown to have undergone frequent and large changes during our sample period. The co-movements for business-cycle frequencies are generally different from those for other frequencies. We find a significant relationship between the time-varying wavelet measure of synchronization and trade only for business-cycle frequencies. The co-movements at longer frequencies are negatively related to trade, so that the overall co-movements and trade tend not to be significantly related.

We focus on changes in dynamic correlation during the recent financial crisis. The results show different responses to this symmetric shock in V4 countries. We discuss possible specialization if the dynamic correlation increases only at certain of the frequencies. Especially, in case of the Czech Republic where the variability of dynamic correlation in business cycle frequencies increased in relation to the euro area, whereas decreased in relation to Germany. Consequently, we point out to the limitations of a correlation and concordance index as common indicators of business cycle synchronization in time domain.

The issue of modelling the economic cycle is important especially in the context of the stabilizing function of economic policy. The identification of different phases of the cyclical fluctuations in economic activity, including the turning point is crucial, not only for the implementation of monetary and fiscal policy at the level of the individual economies, but also in the broader context of the economic integration process, especially from the perspective of the theory of the optimum currency areas (the OCA). The rate of accuracy of the identification of cyclical fluctuations in economic activity, including the turning points, increases the monetary and fiscal policy implementation efficiency, especially the symmetric and asymmetric shocks identification

The purpose of our paper is to define rules for decision of existence spurious synchronization of countries within the currency area. We devote this new methodological approach from an empirical research based on the variability of a dynamic correlation (correlation in frequency domain). We analyze the dynamic correlation in full range and in the business cycle frequencies as well. We also consider lags in economic activity co-movements. Contrary to the standard approach we show its insufficiency especially in case of time domain instruments. For this goal GDP values in quarters of the four Visegrad countries and the Eurozone in the period 1997/Q1-2011/Q1 are used.

Presented paper focuses on consideration and evaluation of methodical approaches to analyze cyclical structure character of economic activity in transition economy. As a starting point, work in time domain is applied, which is followed in frequency domain approach. Both approaches are viewed from methodical as well as application point of view and their advantage and disadvantage are discussed. Consequently, time-frequency domain approach is added and applied on real data. On the basis of obtained results recommendation is formulated. All discussed methodical approaches are also considered from the perspective of capability to evaluate behaving of business cycle in time of global economic crisis before/after year 2008. The empirical part of the paper deals with data of gross domestic product in the Czech Republic in 1996/Q1-2010/Q2.

The paper provides the methodological background for the Czech Republic business cycle dating process using an alternative approach. This approach is based on the mathematical principle of identification of extremes using estimates of derivations of time trend of the analysed time series, for which the nonparametric Gasser-Muller estimate is used. The presented methodological approach is applied on the real gross domestic product data sets, the total industry (excluding construction), the gross capital formation and the final consumption expenditure. The selected variables are taken from the national accounts system. The obtained results are compared to the widely used naive technique of business cycle dating written by Canova (1998, 1999) or Bonenkamp (2001). The presented new method specifies the identification of turning points in the business cycle dating process.

Kernel smoothers belong to the most popular nonparametric functional estimates used for describing data structure. They can be applied to the fix design regression model as well as to the random design regression model. The main idea of this paper is to present a construction of the optimum kernel and optimum boundary kernel by means of the Gegenbauer and Legendre polynomials.

V přispěvku je testovana hypoteza, zda existuje negativni zavislost mezi casovou řadou výnosu z výběru daně z přijmu korporaci a casovou řadou výnosu z výběru daně z přijmu fyzických osob a domacnosti v clenských statech Hospodařske a měnove unie (HMU) a Ceske republice. V ramci provedene kointegracni analýzy nebyla, až na jedine Nizozemi, prokazana u clenských statů HMU existence negativni zavislosti casových řad na 5% hladině významnosti. Lze se tedy domnivat, že ve větsině připadů soucasna daňova soutěž panujici v oblasti korporativniho zdaňovani v clenských statech Evropske unie nevede k přesunu daňoveho břemene z korporaci na fyzicke osoby. Rozdilnost daně z přijmu korporaci v jednotlivých clenských zemich odraži rozdilne ekonomicke podminky - země aplikujici vyssi sazby daně nabizi kvalitnějsi pracovni silu a stabilni podnikatelske prostředi, nově vstupujici země využivaji nižsich sazeb daně aby se etablovali na vnitřnim rozvinutem trhu Evropske unie.

We provide the wavelet analysis of the economic cycle synchronization during the recent fi nancial crisis. How- ever, the global fi nancial crisis caused economic cycles in most European countries to become more strongly synchronized without increasing of the real convergence process. Our contribution is an application of the singular value decomposition to identify and remove the long-term trend including outliers appearing in the year 2007-2010. We found that the histori- cally greater integration provides more highly synchronized cycles in the core Euro area member countries.