The Structure of Consumer Basket in the Czech Republic and Slovak Republic

Purpose of the article: Nowadays, consumer behaviour is still at the centre of attention of many researchers. The consumer basket belongs among important economic characteristics, which determine the economic level of each country. The contribution of the article consists in identification of changes in the structure of consumer basket related to two chosen countries. Methodology/methods: The development of the structure of consumer basket of average household in two countries during the period from 2004 to 2014 is analysed. The structure is expressed by means of expenditure shares, while the development by means of trend models. Coefficient of determination and correlation coefficient are used within choosing the appropriate trend function. Scientific aim: The aim of this article is to assess the development of the structure of consumer basket of average household in the Czech Republic and Slovak Republic during the period from 2004 to 2014 by each country including mutual comparison. In detail, the development of consumer expenditure groups of consumer basket is assessed. Findings: Expenditure shares are found to be enough volatile in time. The highest coefficients of determination are found just in case of quadratic function. Mostly, the found correlation in trend model is strong. Incomes and expenditures mostly increase in time. Based on the 2004 and 2012 comparison, the percentage rates expressing, how much incomes exceed expenditures increase about 11% by the household in the Slovak Republic, however the ones increase only about 3% by the household in the Czech Republic. Conclusions: The structure of consumer basket of household and the structure of household expenditures in the Slovak Republic differs from the ones in the Czech Republic. Both differences and common features are found within the development of indicators. Common features could be caused by the fact, that these two countries constituted only one country till 1. 1. 1993

Stochastically perturbed bred vectors in multi-scale systems

The breeding method is a computationally cheap way to generate flow-adapted ensembles to be used in probabilistic forecasts. Its main disadvantage is that the ensemble may lack diversity and collapse to a low-dimensional subspace. To still benefit from the breeding method's simplicity and its low computational cost, approaches are needed to increase the diversity of these bred vector (BV) ensembles. We present here such a method tailored for multi-scale systems. We describe how to judiciously introduce stochastic perturbations to the standard bred vectors leading to stochastically perturbed bred vectors. The increased diversity leads to a better forecast skill as measured by the RMS error, as well as to more reliable ensembles quantified by the error-spread relationship, the continuous ranked probability score and reliability diagrams. Our approach is dynamically informed and in effect generates random draws from the fast equilibrium measure conditioned on the slow variables. We illustrate the advantage of stochastically perturbed bred vectors over standard BVs in numerical simulations of a multi-scale Lorenz 96 model.Comment: accepted for publication in Q.J.R. Meteorolog. So

Growth and Value Investment Strategy Applied on Chosen Stocks of the New York Stock Exchange

Purpose of the article: Nowadays, investors use many investment strategies. They can realize different profits using different strategies because of different principles of strategies. Author assesses two investment strategies. Calculating different financial indicators leads to comparison of yield and risk of indexes related to these strategies. Presented results could be important for investors within their investment decision in order to create investment portfolio. Methodology/methods: Growth and value investment strategies are theoretically described and applied in real data within 2008–2012. Using the CAPM model, author divides stocks of the NYSE included in the base of the DJIA into growth stocks and value stocks. Author compares index trends in charts, interpolates individual index charts by trend line and calculates financial indicators. Scientific aim: The aim of the article is to assess growth and value investment strategies which are applied to chosen stocks traded on the NYSE within 2008–2012. Author compares yield and risk of growth index with yield and risk of value index and DJIA index. Findings: Author applies growth and value investment strategies to chosen stocks. Sharpe ratio of indexes within whole period 2008–2012 is negative, whereas Jensen’s alpha is positive. Information ratio is positive only within 2008. Value investment strategy has lead to higher yield than growth investment strategy since October 2010, whereas before this month values had not been so different, but rather similar. Risk of value index is higher than risk of growth index and smaller than risk of DJIA index within each year of whole period 2008–2012. Conclusions: Similarly to results of empirical studies cited in this article, results of author indicate that value stock yields are higher than growth stock yields. Based on assessment of these investment strategies, investors could use results when they are making investment decision

Central limit theorems and suppression of anomalous diffusion for systems with symmetry

We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly expanding maps. In particular, our results include situations where the central limit theorem would fail, and anomalous behaviour would prevail, if the compact group were not present. This has important consequences for systems with noncompact Euclidean symmetry and provides the rigorous proof for a conjecture made in our paper: A Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Proc. Natl. Acad. Sci. USA 110 (2013) 8411-8416.Comment: Minor revision

Broadband nature of power spectra for intermittent Maps with summable and nonsummable decay of correlations

We present results on the broadband nature of the power spectrum $S(\omega)$, $\omega\in(0,2\pi)$, for a large class of nonuniformly expanding maps with summable and nonsummable decay of correlations. In particular, we consider a class of intermittent maps $f:[0,1]\to[0,1]$ with $f(x)\approx x^{1+\gamma}$ for $x\approx 0$, where $\gamma\in(0,1)$. Such maps have summable decay of correlations when $\gamma\in(0,\frac12)$, and $S(\omega)$ extends to a continuous function on $[0,2\pi]$ by the classical Wiener-Khintchine Theorem. We show that $S(\omega)$ is typically bounded away from zero for H\"older observables. Moreover, in the nonsummable case $\gamma\in[\frac12,1)$, we show that $S(\omega)$ is defined almost everywhere with a continuous extension $\tilde S(\omega)$ defined on $(0,2\pi)$, and $\tilde S(\omega)$ is typically nonvanishing.Comment: Final versio