This paper focuses on analysing and modelling inflation and its dynamics in Czech Republic applying a special kind of econometric models. Firstly economic theory of inflation is mentioned - fundamental terms, measuring methods of inflation, the way Czech national bank is monitoring the inflation and obviously a short summary of historical evolution of inflation in Czech economy. In the second part of this paper two econometric concepts of modelling time series are introduced - vector autoregression models (VAR models) and volatility models, concretely ARCH and GARCH models. In connection with the VAR models, Granger causality, impulse response functions, cointegration and error correction models are described. The empirical part includes application of selected models on real time series of chosen macroeconomic indicators. The estimation outputs are interpreted and forecasts are implemented. The quality of chosen econometric models for modelling inflation in Czech Republic is discussed.

Causal inference may help us to understand the underlying mechanisms and the risk factors of diseases. In Genetics, it is crucial to understand how the connectivity among variables is influenced by genetic and environmental factors. Family data have proven to be useful in elucidating genetic and environmental influences, however, few existing approaches are able of addressing structure learning of probabilistic graphical models (PGMs) and family data analysis jointly. We propose methodologies for learning, from observational Gaussian family data, the most likely PGM and its decomposition into genetic and environmental components. They were evaluated by a simulation study and applied to the Genetic Analysis Workshop 13 simulated data, which mimic the real Framingham Heart Study data, and to the metabolic syndrome phenotypes from the Baependi Heart Study. In neuroscience, one challenge consists in identifying interactions between functional brain networks (FBNs) - graphs. We propose a method to identify Granger causality among FBNs. We show the statistical power of the proposed method by simulations and its usefulness by two applications: the identification of Granger causality between the FBNs of two musicians playing a violin duo, and the identification of a differential connectivity from the right to the left brain hemispheres of autistic subjects. / Inferência causal pode nos ajudar a compreender melhor as relações de dependência direta entre variáveis e, assim, a identificar fatores de riscos de doenças. Em Genética, a análise de dados agrupados em famílias permite investigar influências genéticas e ambientais nas relações entre as variáveis. Neste trabalho, nós propomos métodos para aprender, a partir de dados Gaussianos agrupados em famílias, o mais provável modelo gráfico probabilístico (dirigido ou não dirigido) e também sua decomposição em dois componentes: genético e ambiental. Os métodos foram avaliados por simulações e aplicados tanto aos dados simulados do Genetic Analysis Workshop 13, que imitam características dos dados do Framingham Heart Study, como aos dados da síndrome metabólica do estudo Corações de Baependi. Em Neurociência, um desafio consiste em identificar interações entre redes funcionais cerebrais - grafos. Nós propomos um método que identifica causalidade de Granger entre grafos e, por meio de simulações, mostramos que o método tem alto poder estatístico. Além disso, mostramos sua utilidade por meio de duas aplicações: 1) identificação de causalidade de Granger entre as redes cerebrais de dois músicos enquanto tocam um dueto de violino e 2) identificação de conectividade diferencial do hemisfério cerebral direito para o esquerdo em indivíduos autistas.

This thesis investigates if Environmental, Social and Governance (ESG) investments can be considered as an independent asset class. As ESG and responsible investing has increased substantially in recent years, responsible investments have entered the portfolios with other asset classes too. Therefore, there is a need in studying ESG investment properties with other financial asset classes. By collecting daily price data from October 2007 to December 2018, we research the directionalities between ESG, ethical, conventional, commodities and currency. Initially, we employed a MODWT, multiscale investment horizon wavelet analysis transformation of the data. The decomposed wavelet data is then applied in pairwise linear and non-linear Granger causality estimations to study the directionality relationships dependent on investment horizon. Additionally, econometric filtering processes have been employed to study the effects of volatility on directionality relationships. The results mainly suggest significant directionality relationships between ESG and the other asset classes. On the medium-term investment horizon, almost all estimations indicate strict bidirectionality. Thus, on the medium-term, ESG can be said to be integrated with the other asset classes. For the long-term horizon, most relationships are still predominantly bidirectional between ESG and all other asset classes. The biggest differences are found on the short-term horizon, with no directionality found between ESG and commodities that cannot be explained by volatility. Furthermore, most directionality relationships also disappear when controlling for the volatility transmission between ESG and currency on the short-term horizon. Thus, our findings suggest significantly more integration between ESG and ethical and conventional as bidirectionality overwhelmingly prevails regardless of investment horizon. As previous research has found similarities between ethical and conventional as well as ESG having similar characteristics to commodities as conventional and ethical, we suggest that ESG should be considered as being integrated and having strong similarities with other equities. Thus, it should be treated as being part of the conventional equity asset class. Deviations from bidirectionality could be caused by ESG variable specific heterogeneity. However, despite our rejection of ESG as an independent asset class, it still carries significant potential as it excludes firms with climate-harming practices, thereby helping in combating climate-related as well as social and governance issues the world is facing.

This thesis has studied short and long-term dependence structures between European stock markets. Johansen's test for cointegration and Granger's test for non-causality have been applied in order to measure the degree of financial integration in Europe. The cointegration analysis has employed a comparative perspective in which different countries with different institutional adaptation to the economic cooperation within Europe have been considered. The study finds strong support for the existence of cointegration between the Belgian, Norwegian, Swiss and British stock markets in the period after the launch of the euro. This result indicates that financial integration has increased in Europe since no cointegration was identified prior to the introduction of the euro. However, it is more difficult to determine to what extent the European financial cooperation has affected the degree of integration because of the difficulties with isolating formal treaties contribution to the stationary equilibrium. Both the EU and the euro's importance may have affected the integration process, but this thesis finds that this is not the only explanation. Thus, it is more likely that the liberalization of financial markets and the overall integration process best explain the increase in financial integration. The most significant finding is that the cointegrated stock markets in the long-term can be regarded as a regional financial market characterized by similar systematic risk factors. This has implications for both policy-makers who adjust existing policies in Europe and investors looking to allocate portfolios in an efficient manner.

國內有許多以不同資料、次市場劃分以及控制品質的方法編製房地產相關價格指數，提供不同的價格資訊，然而編製的過程可能產生偏誤，影響價格指數之準確性，導致房價指數變動與市場訊息不符，因此各種相關房價指數之市場代表性仍有待釐清。 本文首先觀察目前市場較常使用之信義房價指數(中古屋)及國泰房地產指數(預售屋及新成屋)，發現近年來信義房價指數無法適當反應房地產市場景氣繁榮的情形。此二房價指數領先落後的關係亦不符合相關理論及過去實證，因此認為此二房價指數長期趨勢受到編製資料及估計方法上的偏誤所影響。接著利用政府(房地產交易價格簡訊)及業者(台灣不動產成交行情公報)資料以特徵價格法重新建立台北市及台北縣中古屋房價指數，並與信義房價指數作比較，結果顯示本文建立之中古屋房價指數相對於信義房價指數較符合市場變動與相關訊息。最後，為求未來房地產資訊之應用，將過去相關房價指數研究成果與本文建立之房價指數整合，並驗證台北市國泰房地產指數領先整合中古屋房價指數一季，台北縣國泰房地產指數領先整合中古屋房價指數二季，顯示此台北都會區的中古屋及預售屋房價指數相互間的關係符合相關理論推導與過去實證結果。 / There are many real-estate related price indices established in various formation of datum, submarkets and modeling, providing different kinds of price information. But the process itself may be a victim of error, hence affecting the precision of price indices and cause discrepancy between price indices’ variation and correlative market information, therefore the representativeness of real-estate related price indices must be clarified. In this study, we observe the commonly used Sinyi Housing Price Index (existing housing) and Cathay Real-Estate Price Index(pre-sales and new housing), and discovered that Sinyi Housing Price Index is incapable of reflecting the recent boom in the real-estate market. The Granger Causality test result of these two housing price indices(HPI) is inconsequent to relevant theory and empirical studies, therefore attribute this to the error within the establishment of HPI. Then, we reestablish existing housing HPI of Taipei city and Taipei county by using government and enterprise organized data. In comparison to Sinyi Housing Price Index, our newly established HPI cohere with correlative market information. And last, for future application of real-estate market information, we integrate empirical studies in the past with ours and examine its lead-lag relation with Cathay Real-Estate Price Index. The Granger Causality test result corresponds to relevant theory and empirical studies, furthermore, we found that the time-gap between Cathay Real-Estate Price Index and the Integrated existing housing HPI in Taipei city is 1-season, and 2-season in Taipei county.

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Baigiamajame magistro darbe yra nagrinėjamas Baltijos šalių – Lietuvos, Latvijos ir Estijos BVP, jo kitimo tendencijos bei pagrindiniai makroekonomikos rodikliai – galutinio vartojimo išlaidos, prekių ir paslaugų importas bei eksportas, investicijos, užimtųjų darbo rinkoje skaičius bei BVP defliatorius. Išnagrinėti šių rodiklių apibrėžimai bei ekonominė prasmė, taip pat apžvelgta sukaupta mokslininkų patirtis modeliuojant juos. Siekiant išsiaiškinti ryšius tarp šių rodiklių atlikta koreliacijų bei Grangerio priežastingumo analizė. Modeliuojant, visų pirma, rasti ilgalaikiai sąryšiai tarp kintamųjų, o po to kiekvienai šaliai specifikuotas paklaidų korekcijos modelis bei įvertintas šio modelio tikslumas. Išnagrinėjus praktinius ir teorinius aspektus, pateikiamos baigiamojo darbo išvados ir pasiūlymai. Darbą sudaro 5 dalys: įvadas, analitinė - metodinė dalis, tiriamoji dalis, išvados ir pasiūlymai, literatūros sąrašas. Darbo apimtis – 112 p. teksto be priedų, 60 iliustr., 35 lent., 28 bibliografiniai šaltiniai. Atskirai pridedami darbo priedai. / The gross domestic product of the Baltic States – Lithuania, Latvia and Estonia, has been examined in the master thesis. Trends of the GDP and the main macroeconomic indicators – gross final consumption expenditure, imports and exports of goods and services, investment, labor force and GDP deflator have been analyzed. The definitions of these indicators and an economic sense, as well as researchers' experience in modeling, have been examined. In order to establish the relationship between these variables, analysis of the correlation and Granger causality test has been performed. In particular, modeling started with the finding of the long – term relationship between selected indicators. After that the error correction model has been specified and the accuracy of this model has been estimated. After the examination of the practical and theoretical aspects, the conclusions and recommendations have been presented. Structure: introduction, analytical – methodical part, research part, conclusions and suggestions, references. Thesis consists of: 112 p. text without appendixes, 60 pictures, 35 tables, 28 bibliographical entries. Appendixes included.

In a large number of applications arising in various fields of study, time series are approximated using linear MMSE estimates. Such approximations include finite order moving average and autoregressive approximations as well as the causal Wiener filter. In this dissertation, we study two topics related to the estimation of wide sense stationary (WSS) time series using linear MMSE estimates. In the first part of this dissertation, we study the asymptotic behaviour of autoregressive (AR) and moving average (MA) approximations. Our objective is to investigate how faithfully such approximations replicate the original sequence, as the model order as well as the number of samples approach infinity. We consider two aspects: convergence of spectral density of MA and AR approximations when the covariances are known and when they are estimated. Under certain mild conditions on the spectral density and the covariance sequence, it is shown that the spectral densities of both approximations converge in L2 as the order of approximation increases. It is also shown that the spectral density of AR approximations converges at the origin under the same conditions. Under additional regularity assumptions, we show that similar results hold for approximations from empirical covariance estimates. In the second part of this dissertation, we address the problem of detecting interdependence relations within a group of time series. Ideally, in order to infer the complete interdependence structure of a complex system, dynamic behaviour of all the processes involved should be considered simultaneously. However, for large systems, use of such a method may be infeasible and computationally intensive, and pairwise estimation techniques may be used to obtain sub-optimal results. Here, we investigate the problem of determining Granger-causality in an interdependent group of jointly WSS time series by using pairwise causal Wiener filters. Analytical results are presented, along with simulations that compare the performance of a method based on finite impulse response Wiener filters to another using directed information, a tool widely used in literature. The problem is studied in the context of cyclostationary processes as well. Finally, a new technique is proposed that allows the determination of causal connections under certain sparsity conditions.

Purpose: The purpose of this thesis is to study the causal relationship between bank sector development and economic growth in four Nordic countries (Sweden, Finland, Denmark and Norway). Method: Our thesis is based on a quantitative method. The study consists of a compilation and analysis of key financial indicators that represent economic growth and bank sector development. A Granger causality test has been conducted on the time series in order to measure the causal link between economic growth and bank sector development. Theoretical framework: The study is based on the theory of endogenous growth and the causal relationship between bank sector development and economic growth also known as the demand following and supply leading hypothesis.  Results: The results of the four countries are ambiguous. Except for Denmark, that follows the supply leading hypothesis, the remaining countries do not show a unanimous result.

Functional magnetic resonance imaging (fMRI) has emerged as the method of choice to non-invasively investigate brain function in humans. Though brain is known to act as a nonlinear system, here has not been much effort to explore the applicability of nonlinear analysis techniques to fMRI data. Also, recent trends have suggested that functional localization as a model of brain function is incomplete and efforts are being made to develop models based on networks of regions to understand brain function. Therefore this thesis attempts to introduce the twin concepts of nonlinear dynamics and network analysis into a broad spectrum of fMRI data analysis techniques. First, we characterized the nonlinear univariate dynamics of fMRI noise using the concept of embedding to explain the origin of tissue-specific differences of baseline activity in the brain. The embedding concept was extended to the multivariate case to study nonlinear functional connectivity in the distributed motor network during resting state and continuous motor task. The results showed that the nonlinear method may be more sensitive to the desired gray matter signal. Subsequently, the scope of connectivity was extended to include directional interactions using Granger causality. An integrated approach was developed to alleviate the confounding effect of the spatial variability of the hemodynamic response and graph theory was employed to characterize the network topology. This methodology proved effective in characterizing the dynamics of cortical networks during motor fatigue. The nonlinear extension of Granger causality showed that it was more robust in the presence of confounds such as baseline drifts. Finally, we utilized the integration of the spatial correlation function to study connectivity in local brain networks. We showed that our method is robust and can reveal interesting information including the default mode network during resting state. Application of this technique to anesthesia data showed dose dependent suppression of local connectivity in the default mode network, particularly in the frontal areas. Given the body of evidence emerging from our studies, nonlinear and network characterization of fMRI data seems to provide novel insights into brain function.