Abstracts

ABSTRACTS

Interpretation of the Annual Rate of Inflation

Josef Arlt, Markéta Arltová

Abstract

Inflation is in present time one of the most frequently applied economic terms in Czech Republic. The computation of the consumer price index is based on Laspeyres formula. On its basis the quarterly and annual rate inflation can beconstructed. The annual rate of inflation is the product of four quarterly rates of inflation. The interpretation of the time behaviour of the annual rate of inflation is problematic even if from the point of view of its construction the shape of time series islogic. When this time series is published separately it evokes impression that the dynamic of the growth of the consumer price index has the same shape. While from the time series of the quarterly rate of inflation it is possible to create relativelysimply the picture of the shape of time series of the consumer price index, the movement of the annual rate of inflation do not show it clearly.

On Stablity of Equilibrium in a Model of Net Value Added in Enterprise – an Optimal Control Problem

Andrej Balciar

Abstrakt

V článku je uvedený model čistej pridanej hodnoty v podniku ako rozšírenie modelu čistých peňažných tokov, vytvoreného R. J. Barrom a X. Sala-i-Martinom. Vlastným prínosom je zahrnutie rôznych foriem financovania investícií, predpokladendogénnosti efektívnej mzdovej sadzby a predpoklad, že zadlženosť podniku je klesajúcou funkciou pomeru kapitálu a investícií. Pontryaginov princíp maxima sa používa na maximalizáciu súčasnej hodnoty čistej pridanej hodnoty pomocou efektívnej práce a investícií. Vlastným prínosom je vyšetrovanie stability rovnovážneho stavu v tomto modeli.

Abstract

In the paper a model of net value added in enterprise is introduced as an extension of a model of net cash flow, designed by R. J. Barro and X. Sala-i-Martin. In our contribution various forms of investment financing are incorporated in the model, effective wage rate is assumed to be endogenous, debt-to-capital ratio is assumed to be a decreasing function of capital in relation to investment. The Pontryagin principle of maximum is utilized to maximize the present-value net value added with the help of effective labor and investment. In our contribution the stability of equilibrium in this model is examined.

Key words

Equilibrium, net value added, Pontryagin principle of maximum, saddle-path stability of equilibrium.

Hypothesis testing of Slovak capital market efficiency

Jaroslav Barochovský, Mária Kanderová

Abstrakt

Príspevok sa venuje problematike, či slovenský kapitálový trh spĺňa predpoklady efektívneho trhu, pričom sme sa zamerali na testovanie slabej formy efektívnosti. Pri testovaní efektívnosti slovenského kapitálového trhu sme vychádzali z denného vývoja indexu SAX. Pre overenie predpokladov efektívnosti sme použili Dickey-Fullerov test a korelačné testy.

Abstract

Contribution discusses the Slovak capital market efficiency topic. We tried to find out, whether Slovak capital market verifies assumptions of efficiency market, where we focused to testing of weak efficiency form. While testing Slovak capital market efficiency we came out from daily development of SAX index. To verify efficiency assumptions we used Dickey-Fuller test and correlation tests.

Key words

Efficiency Market Hypothesis, Random Walk Model, stationarity of revenues, Dickey-Fuller test

Probability Models of Income Distribution

Jitka Bartošová

Abstract

Probability models of income distribution provide for evaluation of the living standard of population of a country at whole as well as for comparison of the living standard of different social classes or regions in the country. For creation of a probability model it is important both, to find a theoretical distribution function that characterizes empirical frequency distribution and to choose suitable methods to calculate parameters of the model. To construct a suitable parametric model of income distribution one can apply the maximization of coincidence of theoretical and empirical fraquencies or quintiles. This paper concentrates on methods of probability modeling and their application to creation of a model of household income distribution.

Key words

Income distribution; probability model; validity of the model

Bayesian Curve Fitting using Piecewise Polynomials

Dariusz Biskup

Abstract

The paper presents a nonparametric procedure for estimation of an unknown regression function f in the regression model:

.

The regression function is expressed as a composition of a certain number of low order polynomials defined on intervals separated by the so called knot points. The Bayesian estimation of the regression function allows the number and the location of the knot points to be random variables which are estimated using the data.

The paper presents several application of this method which use Markov Chain Monte Carlo techniques.

Key words

Bayesian model selection, curve fitting, piecewise polynomials, Markov Chain Monte Carlo.

Outliers in Regression

Dagmar Blatná

Abstakt

Odlehlá pozorování (outliers) a vlivné body (leverage points) hrají významnou roli pro výsledky regrese. Vlivné body (vybočující pozorování v hodnotách X) jsou bud “dobré” nebo “špatné” podle jejich vlivu na regresní odhady. Existuje celá řada měr a metod, pomocí nichž můžeme identifikovat odlehlá pozorování a vlivné body. Většinou se jedná o kombinaci numerických a grafických metod.

Abstract

Outliers play important role in regression. It is pertinent to distinguish between vertical outliers (outliers in the y-direction) and so-called leverage points (outliers in x-direction). There are two types of leverage points: good and bad. A good leverage point is a one that is unusually large or small among the X values but is not a regression outlier. Several diagnostic measures have been designed to detect individual cases or group of cases that may differ from the bulk of the data. The field of diagnostic consists of a combination of numerical and graphical tools.

Key words

Regression, robust methods, outliers, detection of outliers.

Využití neparametrických rozdělení při modelování finančních rizik

Martin Cícha, Pavel Zimmermann

Abstrakt

Příspěvek  se věnuje novým možnostem využití stochastických procesů ve spojitém čase při modelování finančních rizik. V příspěvku je snaha využít neparametrická rozdělení a odbourat tak alespoň z části neověřitelné a nezdůvodněné předpoklady běžných modelů. Příspěvek bude zaměřen zejména na problematiku modelování úrokových měr.

Abstract

This paper describes new possibilities of  using time continuous stochastic processes in financial risk  modeling. This paper is trying to use nonparametric distributions to remove some unverifiable assumptions of common models. The paper will be focused on interest ratemodelling.

Key words

Nonparametric distributions, Time continuous stochastic processes

Armand Borel

Jan Coufal

Abstract

Armand Borel (* 21 May 1923, La Chaux-de-Fonds, Swiss  – + 11 August 2003, Princeton, New Jersey, USA) was a Swiss mathematician, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups. (He used to answer the question of whether he was related to Émile Borelalternately by saying he was a nephew, and no relation.)

He studied at the ETH Zürich. He came under the influence of the topologist Heinz Hopf, and the Lie group theorist Stiefel. He was in Paris from 1949 – he applied the Leray spectral sequence to the topology of Lie groups and their classifying spaces, under the influence of Leray and Henri Cartan.

He collaborated with Jacques Tits in fundamental work on algebraic groups, and with Harish-Chandra on their arithmetic subgroups. In an algebraic group G a Borel subgroup H is one such that the homogeneous space G/H is a projective variety, and as small as possible. The Borel–Moore homology theory applies to general locally compact spaces, and is closely related to sheaf theory. He published a number of books, including work on the history of Lie groups.

Czech Economic Growth in the Context of National Accounts

Jakub Fischer, Jaroslav Sixta

Abstract

The aim of this paper is to show basic consequences of economic growth and the following benefits for the country. For these purposes, a brief description of the structure of national accounts is given. The core of the problem of economic growth consists in distribution of benefits. This issue is described by the difference between gross domestic product and gross national income, which is influenced by the relationships between residents and non-residents. Analyses of gross national income in central Europe will become more important in the near future because of ongoing economic linking. This linking means mainly foreign direct investments and foreign labour force that affect both gross domestic product and gross national income, which is moreover influenced by transfers of profits and wages.

Key words

Gross domestic product, gross national income, economic growth, foreign direct investments.

FORWARD-LOOKING TAYLOR’S RULE APPLIED ON SLOVAK CONDITIONS

Rudolf Gavliak, Vladimír Úradníček, Emília Zimková

Abstract

Taylor’s rule is a formula developed by Stanford economist John Taylor. It was designed to provide “recommendations” how a central bank should set short-term interest rates as economic conditions change to achieve both its short-run goal for stabilizing the economy and its long-run goal for inflation. Real short-term interest rate should be set according to the main considerations: position of actual inflation relative to the targeted level and the stage of the output gap. In the contribution the modified forward-looking Taylor rule is applied on Slovak conditions.

Key words

Taylor’s rule, Inflation targeting, Output gap

Analysis of Dispersion Effects in Experimental Design

Eva Jarošová

Abstract

The paper deals with the analysis of an experiment for robust design. In the robust design two kinds of factors are considered, i.e. control and noise factors. The noise factors vary during the process and account to an increased variability of the response variable. The aim of the robust design is to set the control factors to such levels so that variability of the response variable caused by noise factors was decreased. To ensure this, control factors which affect the response variability have to be found. Two modelling strategies can be used. Either the response variable is modelled in dependence on both the control and noise factors, or the response mean and variance are modelled simultaneously. The aim of the paper is to review methods used in robust design. Different methods are compared in view of their efficiency. As an example that illustrates the problem data reported in literature are reanalyzed.

How much taxed are expenditures of the Czech households?

Stanislav Klazar, Barbora Slintakova, Slavomira Svatkova, Martin Zeleny

Abstract

The paper presents the research undertaken by the research team in an attempt to model the impact of the taxes on consumption on Czech households. We apply the microsimulation technique on the household expenditure microdata from Czech Household Budget Survey. The paper presents the methodology used to model the taxation and the analytical possibilities of the constructed model, together with the first initial results of its application on the analysis of VAT taxation inCzech republic.

CALCULATION OF THE AOQL PLANS BY VARIABLES WITH THE USE OF NON-CENTRAL  t  DISTRIBUTION

Jindřich Klůfa

Abstract

In this paper we shall deal with the AOQL single sampling plans for inspection by variables when the remainder of rejected lots is inspected. We shall report on an algorithm allowing calculation of these plans in case when the non-central t distribution shall be used for operating characteristics. Calculations of these plans is very difficult, for the calculation we shall use an original method.

Kdy by se mělo odcházet do důchodu?

Felix Koschin

Abstract

About ten years ago, there was an intensive political debate on shifting the pension-age in the Czech Republic. The result was a moderate gradual rising of the age. Now it is clear that it will not be sufficient but doubts exist whether the older people will be enough healthy to work. The healthy life expectancy and its forecast give the answer – the pension-age could be as high as 70 years of age.

Correspondence Analysis and Log-linear Analysis of Economical Situation of Micro-Companies in Wroclaw Agglomeration

Cyprian Kozyra

Abstract

Correspondence analysis and log-linear analysis are two different philosophically approaches to analyze contingency tables. Correspondence analysis is exploratory technique and log-linear analysis is confirmative model-based method. There is considered in the paper association between these two analyses and presented application on data from labor market research in Wroclaw agglomeration.

Key words

Correspondence Analysis, Log-linear Analysis, Wroclaw Agglomeration, Labor Market, Contingency Table.

Inflation expectations of Slovak consumers

Petr Laco, Žaneta Lacová

Abstract

Overall level of inflation expectations in population can be derived from consumers’ surveys. Consumers are asked for their anticipation of price level changes. Our paper focuses on prediction potential of such expectations in Slovakia. In addition, a central bank point of view is stressed: we analyze whether these expectations react on the monetary impulses of slovak monetary policy, e.g. whether they fulfill rationality conditions.

On Bifurcations in Schinasi´s Business Cycle Model

Katarína Makovínyiová

Abstract

In this paper Schinasi´s business cycle model is thoroughly analysed. It is a three dimensional model, which describes the development of output, interest rate and money supply in a closed economy. We find the sufficient conditions for the existence of equilibrium, its stability and the existence of business cycles. Also formulae for the calculation of bifurcation coefficients are derived.

Key words

dynamical model, equilibrium, stability, bifurcation, cycles

Logaritmicko normální rozdělení jako model rozdělení mezd

Luboš Marek, Michal Vrabec

Abstrakt

V našem příspěvku se věnuje možnostem modelování mzdových rozdělení pomocí logaritmicko normálního (LND) rozdělení a s tím souvisejících problémů. Především se věnujeme možnostem odhadů parametrů LND na základě výběrových charakteristik.

Abstract

We build the model for payment distribution with using of lognormal probability distribution.function in our paper. We solve amount of related problems. The topic of our paper is construction of parameter estimations on the basis of sample characteristics for lognormal distribution

Key words

Salary distributions, characteristics of location.

The compound Poisson approximation

Anna Nikodem

Abstract

In this paper the compound Poisson approximation is described. The compound Poisson approximation is a well-known approximation of the total amount of claims in the individual risk model with claims independently and identically distributed. This approximation can also be used for portfolios consisting of n policies without the assumption of independence.

Method of death risk estimation for heterogeneous population

Stanisława Ostasiewicz

Abstract

Ordinary life table assume that population is homogenous. In practice this assumption is usually unrealistic. We know that peoples in the same age are in different way susceptive for death. Factor which determine that individual differ in the mortality risk in my presentation will be called frailty. We assume that frailty is random variable which is a gamma distributed.

Modeling responses

Walenty Ostasiewicz

Abstract

The aim of this paper is to overview statistical models suitable for representation of mechanisms generating answers to questionnaire questions.

Some novelty of this presentation is the treatment of these models within the general methodology of statistical informer. This in turns enable us, among other things, to predict answers and properly classify them. In this paper is undertook also an attempt to distinguish the difference between psychometric and sociometric views on these models.

Kvantifikace vlivu šikmosti základního souboru na rozdělení výběrových statistik při provádění malých výběrů (velikost výběrového souboru n<30)

Roman Pavelka

Abstrakt

Cílem příspěvku je posouzení empirického rozdělení výběrových statistik při provádění malých výběrů (o velikosti výběrových souborů n<30) z kladně zešikmených mzdových rozdělení. Získaná empirická rozdělení výběrových statistik budou porovnána s teoretickými rozděleními – se Studentovým a Gaussovým (normálním) rozdělením. Na závěr bude kvantifikován vliv šikmosti základního souboru na rozdělení výběrových statistik získaných z malých výběrů.

Abstract

The aim of paper is an examination of sample statistics empirical distribution on small-size sampling (for sample sizes up to 30) from positive skewed wage distributions. Obtained sampling distributions of sample statistics will compare with teoretical distributions – with Student and Gauss (normal) distributions. Finally will be quantified the population skewness effect on sample statistics distributions obtained from small-size sampling.

Key words

Klíčová slova :rozdělení výběrových statistik, Gaussovo (normální) rozdělení, Studentovo rozdělení, rozdělení výběrové šikmosti, výběr malého rozsahu

Analysis of Categorical Data from Two Dependent Samples

Iva Pecáková

Abstrakt

Statisticky závislé výběrové soubory pocházejí z opakovaného zjišťování hodnot jedné proměnné v souboru jednotek (dva soubory tvoří tytéž jednotky). Vznikají také v situaci, kdy jednotky ve dvou souborech tvoří přirozenou dvojici (manželský pár, hodnocení téže skutečnosti dvěma osobami, apod.). Obě proměnné nabývají v takové situaci stejných kategorií a jsou-li data tříděna do dvourozměrné kontingenční tabulky, je tabulka čtvercová. Příspěvek se zabývá metodami určenými pro analýzu dat ze závislých výběrů tříděných ve čtvercových kontingenčních tabulkách.

Abstract

Statistically dependent samples are the samples result from repeated observations on the response variable for a set of subjects (two samples that have the same subjects). Such samples also occur in so called matched-pair designs, when two samples have a natural pairing (married couples, two people rate the same fact, etc.). Both variables have the same categories in this situation and if responses are summarized by a two-way contingency table, this table is square. The paper presents analyses methods for dependent samples classified in such square contingency tables.

Key words

categorical variables, matched-pairs

Analysis of Multiple-Response Data

Miroslav Plašil, Petr Vlach

Abstrakt

Příspěvek se věnuje novým metodám při zpracování kategoriálních dat typu mnohonásobné odpovědi. Pozornost je věnována zejména výhodám jejich použití v dotazníkových šetření, testování asociací v kontingenčních tabulkáchs mnohonásobnými odpověďmi a grafické analýze.

Abstract

This paper presents new methods for analyzing categorical multiple-response data. We discuss the advantages of using multiple-response questions in surveys, testing for associations in contingency tables with multiple-response data and graphical analysis.

Key words

Categorical data, Multiple-response data, Chi-square test

Modeling of high-frequency financial time-series

Jiří Trešl2

Abstrakt

Jsou diskutovány a aplikovány metody vhodné pro modelování vysokofrekvenčních finančních časových řad. Zvláštní pozornost je věnována zejména modelům typu GARCH, autoregresním modelům s náhodnými koeficienty a bilineárnímmodelům. Jsou zkoumány možnosti využití stavově-prostorového přístupu jak pomocí simulací, tak reálných finančních časových řad.

Abstract

The methods suitable for the modelling of high-frequency financial time series are discussed and applied. Among them, GARCH models, autoregressive models with random coefficients and bilinear models deserve particular attention. The possibility of employing state-space framework is investigated both using simulations and real financial time-series.

Key words

High-frequency time-series, financial modelling, GARCH models

Statistical Office of Nationally-Economical Society: the Forerunner of Provincial Statistical Office in Bohemia

Prokop Závodský

Abstrakt

Před 150 lety – r. 1856 zřídila Vlastenecko-hospodářská společnost v Čechách výbor pro zemědělskou a lesnickou statistiku a o rok později zahájila činnost statistická kancelář. R. 1898 se stala základem Zemského statistického úřadu v Čechách a přímá vývojová linie vede až k dnešnímu Českému statistickému úřadu.

Abstract

150 years ago – in 1856 – Nationally-Economical Society in Bohemia had established Committee for Agricultural and Forester Statistics and, one year later, Statistical Office started its activity. In 1898, it became the fundament of Provincial Statistical Office in Bohemia and direct line of development leads to contemporary Czech Statistical Office.

Key words

Statistical Office of Nationally-Economical Society: the Forerunner of Provincial Statistical Office in Bohemia

Dynamic optimization of economic processes

Rudolf Zimka

Abstract

In the contribution it will be shown how Pontryagin´s Maximum Principle can be utilized in optimal growth theory with a production function which is not convex.

Note on the Estimators Properties in Case of Imputed Data Sets

Beata Zmyślona

Abstract

The choice of imputation technique has some influence on estimators properties. The most popular methods, like case deletion or deterministic imputation, used to analyse incomplete data are invalid because the estimators are biased and the standard errors are under- or overestimated. In this paper we compare the properties of estimators for various imputation methods based on data augmentation (multiple imputation, parameter simulation). We present the methods which improve the estimator variance.

Key words

Missing data, Bayesian inference, data augmentation, estimator variance, bias of estimators.

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