This thesis focuses on fractal analysis of economic time series. Chapter One introduces fractal analysis as a method of exploring time series and gathers information about progress and current state of understanding in this field. Chapter Two focuses on design and development of computer software, which will calculate selected fractal indices. Chapter Three is experimental and shows the results and discussion of economic time series (popular stock market indexes and currency exchange rate) analysis that have been obtained from the software developed in Chapter Two.

This work discusses estimates based on rounded data. The work describes the estimates of parameters in time series AR and MA and in linear regression, the work presents different kinds of estimates based on rounded data. The work focuses on time series model AR(1) and linear regression, where simulations are added to theories and methods are compared on rounded and unrounded data. In addition, the comparison of linear regression is shown on the exemple of graph data. Powered by TCPDF (www.tcpdf.org)

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

The thesis concentrates on property of linearity in time series models, its definitions and possibilities of testing. Presented tests focus mainly on the time domain; these are based on various statistical methods such as regression, neural networks and random fields. Their implementation in R software is described. Advantages and disadvantages for tests, which are implemented in more than one package, are discussed. Second topic of the thesis is additivity in nonlinear models. The definition is introduced as well as tests developed for testing its presence. Several test (both linearity and additivity) have been implemented in R for purposes of simulations. The last chapter deals with application of tests to real data. 1

This master thesis is focused on analysis and forecasting of hourly and daily electricity price on the deregulated Czech daily electricity market. The methods used for estimating and forecasting hourly and daily prices are picked from the ARIMA-GARCH family of models and Neural Networks. For daily price data, the Redundant Haar Wavelet Transform decomposition of the time series is used in combination with ARIMA and Neural Networks models for forecasting. For hourly data, ARIMA and Neural Network models are considered. The forecasting results of daily data indicate that simpler models such as seasonal ARIMA outperform all other methods. Also the wavelet decomposi- tion of the daily series didn't prove useful in enhancing the forecast precision. For hourly data, the Multilayer Perceptron architecture of the neural network outperformed the ARIMA forecast. JEL Classification C20, C22, C45, C53, C65 Keywords Forecasting, Time Series, ARIMA, GARCH, Neural Net- works, Wavelet Transform Author's e-mail krystof.cerny@gmail.com Supervisor's e-mail lebovicm@gmail.com 1

The aim of this thesis is to analyze the performance of nonlinear threshold models in forecasting the exchange rate of Czech koruna against EUR. Data for this study were obtained from Statistical Data Warehouse of European Central Bank (ECB) website, from Czech National Bank (CNB) Board decisions minutes and from the press releases of Governing Council of ECB. The data set was split into two periods - from 1999 until November, 2013 when CNB started to use interventions and from November, 2013 until April, 2016. Models used in the thesis are Self-Exciting Threshold Auto Regressive (SETAR) models with one and two thresholds and two Threshold Auto Regres- sive (TAR) models with different threshold variables - meetings of CNB Board as dummy variable and average volatility over recent periods. The forecasting results indicate that SETAR models did not outperform Random Walk in any period. TAR models offered promising results in the period before interventions and surprisingly failed in the period during interventions. This study supports the general belief of exchange rates being difficult to forecast and that it holds in case of Czech koruna as well. JEL Classification F12, F21, F23 H25, H71, H87 Keywords forecasting, exchange rate, time series, nonlin- earity, SETAR, TAR Author's e-mail zaka.one@gmail.com...

The thesis deals with a brief compilation of the theory of Fourier transform, linear filtration and a triad of wavelet transforms -- the maximal overlap discrete wavelet transform (MODWT), the discrete wavelet transform (DWT) and the continuous wavelet transform (CWT). These transforms are among others applied to the analysis of the time-varying character of variability in the time series, to the detection of events of significant changes of variability, to the removal of noise in the time series (denoising) and to the time-scale analysis of the relationship of two time series. The analyzed time series used in this thesis are the logarithm of the Garman-Klass estimate of the historical volatility, the time series of stock returns and the logarithm of the monthly inflation rate. In some cases artificial time series are analyzed. The procedures and methods introduced in the thesis might be well implemented in the analysis of other economic and financial time series. The contribution of the thesis is a brief and easy-to-use compilation of the wavelet theory and the application of the wavelet transform to such financial and economic time series, where such an analysis tool has never been applied before. New insights into the properties of time series are thus obtained, insights, which might be hardly recovered by traditional means and methods.

This thesis deals with INGARCH models for a count time series. Main emphasis is placed on a linear INARCH model. Its properties are derived. Several methods of estimation are introduced - maximum likelihood method, least squares method and its modifications - and later compared in a simulation study. Main properties and maximum likelihood estimation for INGARCH(1,1) model are stated. Higher order linear INGARCH models and nonlinear INGARCH models are discussed briefly. An application of the presented models on time series of car accidents is given.

The thesis is aimed at climatological, agroclimatological and phenological conditions at Tušimice observatory during 45 years of observations (1968-2012) on basis of meteorological and phenological data by using statistical methods, method of cumulative series and geographical information system. Basic climatic elements (air temperature, precipitation total, snow cover, cloudiness, wind, humidity, sunshine duration, fog and thunderstorm), agroclimatic characteristics according to the WMO recommendation, selected phenological phases (mainly beginning of flowering 10 %) of herb and wooden species were processed in the study. The literature overview was made on climatic and phenological conditions at Tušimice station, in the Czech Republic and other countries. Apart from statistical analysis, the elements were also evaluated in the interaction with the changing air circulation in Central Europe. In addition, results were compared to Quitt's classification based on long-term averages of meteorological data (1961-1990 versus 1981-2010). The drought occurrence was evaluated in 45 years of observations period. The thesis is divided into three main parts - Climatic conditions of Tušimice observatory (part 5.1), Agroclimatic conditions of Tušimice observatory (part 5.2) and Phenological conditions of...

This thesis analyses the relationship between insider trading regulation (broadly interpreted) and equity costs of firms on data from the Chinese, South African and Russian capital markets covering the years from 1995 to 2011. Time series analysis showed -- as expected -- that stock markets in each of the countries react in specific ways: E.g. none of the regulatory measures proved effective in decreasing the equity costs in the case of South Africa. Analysis of the Chinses and Russian data showed, however, a possible common feature of the participants on the two markets. It seems that these markets react to mere signals of upcoming regulatory measures rather than on these measures themselves. This interpretation of the results is thus in line with the rational expectations hypothesis.