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Application of Kalman Filtering
Svojík, Marek ; Hlávka, Zdeněk (advisor) ; Anděl, Jiří (referee)
The aim of this work is to discuss the use of the Kalman lter in some economical problems. Generally taken, the Kalman lter is a mathematical method (an algorithm) used for estimation of the non-observable component of a state. Especially, this approach will be applied to estimate the risk-neutral state price density of CALL options. In such case a non-linear relation between state and observed variables may be assumed, and the problem has to be linearized by Taylor expansion. In detail, the main Kalman ltering in the simple linear case will be presented in the rst chapter. In the second chapter, you can nd some application of that Kalman ltering in case of CALL options. The study of the extended Kalman lter and its application in case of a nonlinear state model and the use of the Taylor expansion can be found in Chapter 3. In the fourth chapter, we will be talking about estimating the risk-neutral price density of a CALL option. The corresponding outputs from the program R and the most important results of this work are summarized in the last Chapter 5.
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The changing Sweden's regional pattern and its context
Klíma, David ; Tomeš, Jiří (advisor) ; Anděl, Jiří (referee)
Regional disparities and spatial inequality are typical topics studied by geography. Sweden is one of the most homogeneous and egalitarian countries in the world. Simultaneously, it is characteristic for its very low regional disparities and thus it is an important and interesting subject for studying. The main goal of this thesis is to examine changes in a regional pattern from the beginning of the 1990s and to analyse an impact of structural changes (deindustrialization and tertiarization) and globalization (through activities of transnational corporations) on regional disparities. In the thesis socioeconomic and demographic indicators and quantitative statistics are used to analyse a development of regional disparities in Sweden and to examine a broader context of this development. The main finding of the thesis is a disproportional growth of metropolitan regions (mainly Stockholm). Share of metropolitan regions on population and socioeconomic activities is increasing and it is characterized by dynamic development which is intensified by high specialisation, major valued-adding activities, knowledge-based economy and localisation of transnational corporations. Regional variability is slowly increasing and disproportional growth of metropolitan regions contributes to this development. Thus the...
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Effects of the Arab Spring on the Change of Security, Migration and Economic Policy of Selected Countries of the Mediterranean
Výborná, Veronika ; Jelen, Libor (advisor) ; Anděl, Jiří (referee)
The submit diploma thesis is based on the liberal-idealistic international relations research. It attempts to analyze the relationship of selected countries of the North (Europe) and the South (North African) Mediterranean in the context of the Arab Spring. Specifically, it focuses on three different policy where using selected indicators will be examined the relationships. These are policy of security and defense, migration and economic cooperation. The work is based on the idea that mutual peace cooperation, institution building and prosperity leads to the development and stability of the whole region. This approach has been applied in the Mediterranean region since the decolonization of Africa and mutual cooperation, mainly in the economic trade, can be resisted since antiquity. Arab spring which caused destabilization and in some cases of overthrew government had relations disrupt in the Mediterranean region. The mean goal is tracking of potential changes in the relationship between the countries of France, Italy, Spain (as the European Mediterranean countries) and Tunisia, Egypt and Libya (such as the North African Mediterranean countries where there was the political changes in 2011). Currently, not only North African Mediterranean countries, but the entire Middle East is seen as a potential...
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Birthday problem
Drápal, Lukáš ; Anděl, Jiří (advisor) ; Dostál, Petr (referee)
In the presented work we discuss the birthday problem with unlike probabilities. First, we introduce the concept of majorization of vectors, Schur convexity of functions and Bell polynomials. Using these concepts we show the results from papers [6] and [8]. We also discuss the paper [7] and we point out its error. Then we present a program in language R that is simulating the problem. We use this program to calculate the probability for the true birthday problem in the Czech Republic and the effect of leap years. Finally, we show some applications of the birthday problem, especially the true surname problem in Japan [8].
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Tests in multinomial distribution
Holý, Vladimír ; Anděl, Jiří (advisor) ; Antoch, Jaromír (referee)
In this paper there are at first described classical goodness-of-fit tests - the Pear- son's χ2 test and the log likehood ratio test. The more modern method of testing is the family of statistics based on power divergence which is generalisation of classical statistics. Another type of generalisation is the family of disparity statis- tics which includes beside the family of power divergence also the families BWHD and BWCS. It is demonstrated that all these test statistics have an asymptotic χ2 distribution. In the program R the exact level and exact power can be calculated for individual tests. Hereafter, moments of test statistics can be derived. On the basis of these comparisons there will be shown which test statistics are the most suitable for the goodness-of-fit tests. 1
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Bimodal distributions
Došlá, Šárka ; Anděl, Jiří (advisor) ; Dupač, Václav (referee)
We study the bimodality of the mixture of two unimodal distributions. In the special cases we give necessary and su±cient conditions ensuring the bimodality of such mixtures. We study the probability of the event that the histogram of a random sample from unimodal distribution indicates two peaks. For some types of unimodal distributions it is possible to simplify this problem and we can study histograms of samples from uniform distribution instead. We show that for increasing number of observations the probability that histogram with N classes has two peaks tends to the probability that the random permutation of numbers 1;...;N is bimodal.
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Statistical analysis of historical temperature series
Gergelits, Václav ; Antoch, Jaromír (advisor) ; Anděl, Jiří (referee)
Title: Statistical analysis of historical temperature series Author: Václav Gergelits Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jaromír Antoch CSc. Supervisor's e-mail address: antoch@karlin.mff.cuni.cz Abstract: In the present work we deal with the statistical analysis of time-series of a mean-temperature obtained from seven European cities from the Europe Union project "IMPROVE". Properties of the time series are analyzed by means of descriptive statistics, being assessing their homoscedasticity, autocorrelation and normality. We report the ways in which the data has been adjusted, including consideration of the impact of the urban heat island and we discuss the availability of additional data. The theoretical part presents a theory of change point detection for a one change model as well as more than one change model taking an autocorrelation into account. In the practical part we analyze the data using change point detection method. The significant increase was not detected for time series of Cadiz and Uppsala. The significant increase was rather detected for the rest of the time series. The increase of temperature could be in a relation to the adjustment for the urban heat island. Keywords: change point detection, temperature time series 1
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