The recent popularity of Bayesian inference is due to the practical advantages of the Bayesian approach. The Bayesian analysis makes it possible to reflect ones prior beliefs into the analysis. In this thesis, we explore some asymptotic results in Bayesian nonparametric inference for restricted and unrestricted space of distributions. This thesis is divided into two parts. In the first part, we employ the Dirichlet process in a hypothesis testing framework to propose a Bayesian nonparametric chi-squared goodness-of-fit test. Our suggested method corresponds to Lo's Bayesian bootstrap procedure for chi-squared goodness-of-fit test. Indeed, our bootstrap rectifies some shortcomings of regular bootstrap which only counts number of observations falling in each bin in contingency tables. We consider the Dirichlet process as the prior for the distribution of data and carry out the test based on the Kullback-Leibler distance between the Dirichlet process posterior and the hypothesized distribution. We prove that this distance asymptotically converges to the same chi-squared distribution as the classical frequentist's chi-squared test. Moreover, the results are generalized to the chi-squared test of independence for contingency tables. In the second part, our main focus is on Bayesian nonparametric inference for a restricted group of distributions called spherically symmetric distributions. We describe a Bayesian nonparametric approach to perform an inference for a bivariate spherically symmetric distribution. We place a Dirichlet invariant process prior on the set of all bivariate spherically symmetric distributions and derive the Dirichlet invariant process posterior. Indeed, our approach is an extension of the Dirichlet invariant process for the symmetric distributions on the real line to bivariate spherically symmetric distribution where the underlying distribution is invariant under a finite group of rotations. Further, we obtain the Dirichlet invariant process posterior for the infinite transformation group and we prove that it approaches a certain Dirichlet process. Finally, we develop our approach to obtain the Bayesian nonparametric posterior distribution for functionals of the distribution's support when the support satisfies certain symmetry conditions. When symmetry holds with respect to the parallel lines of axes (for example, in two dimensional space x = a and y = b) we employ our approach to approximate the distribution of certain functionals such as area and perimeter for the support of the distribution. This suggests a Bayesian nonparametric bootstrapping scheme. The estimates can be derived based on posterior averaging. Then, our simulation results demonstrate that our suggested bootstrapping technique improves the accuracy of the estimates.

The human cytomegalovirus (CMV) is one of the viruses which extensively infect in the world. In order to grow and reproduce, the CMV invades designated cellular lives and influences their behavior. The origin of replication (also called the replication origin) is a particular sequence in the CMV DNA genome at which replication is initiated. In this study, we develop some statistical tests of complementary palindromes, which can be applied to narrow the search for replication origin of the CMV DNA sequence. Let X_(2k) be the number of complementary palindromes with length 2k and Y_(2k) be the number of non-covered complementary palindromes with length 2k inside a given DNA sequence. Consider the null hypothesis that the marginal probabilities of the four nucleotides remain the same (1/4) over the given sequence versus the alternative hypothesis that the marginal probabilities are different. The likelihood ratio test based on the joint distributions of Y_(18) and Y_(2k) | (Y_(2(k+1)), ...,Y_(18)), where k=1, ..., 8, under the null and the alternative hypotheses are derived. The null distribution of the test statistic is approximated by a scaled chi-squared distribution. The scale parameter and the degree of freedom are estimated by the method of moments. The Pearson's chi-squared test based on the marginal distributions of X_(2k), where k=1, ..., 9. The null distribution of the test statistic is also approximated by a scaled chi-squared distribution. There is an another focus about ratios statistics X_(2k)/X_(2(k+1)) and Y_(2k)/Y_(2(k+1)), which approximate a specific value under the null hypotheses. Simulation studies are performed to confirm the theoretical findings.

Taiwan Security Market is a typical order-driven market, and the business transactions are matched through the electronic trading system since 1988. In this work, we study the joint distributions of tick size changes of bid price and ask price, bid volume, and ask volume¡@for each matching order in Taiwan Stock Exchange (TSEC). Exponentially weighted moving average (EWMA) method is adopted to update the joint distribution of the incoming order variables aforementioned. Here we propose five methods to determine the update timing and consider three different initial matrices of the joint distributions. In empirical study, the daily matching data of two enterprises Uni-president Enterprises Corporation and Formosa Plastics Corporation in April, 2005 are considered. The goodness of fit for the joint distributions are determined by Chi-square Goodness of Fit Test. The results show that EWMA method provide good fit for most of the daily transaction data.

[pt] A análise técnica ou grafismo consiste na identificação visual de padrões geométricos em gráficos de séries de preços de mercado com o objetivo de antecipar tendências de preço. Esta Dissertação revisita a questão da validação estatística da análise técnica, que tem sido estudada na literatura sem os devidos cuidados com os problemas de heterogeneidade e de dependência estatística dos dados analisados - agrupamento de séries de retornos referentes a diversos ativos financeiros distintos. O objetivo central deste estudo consiste em resolver o primeiro problema citado, através de uma metodologia para homogeneizar os ativos no que concerne às distribuições de probabilidades de suas séries de retorno. Os passos gerais desta metodologia envolvem a identificação dos processos estocásticos geradores dos retornos dos ativos, o agrupamento de ativos semelhantes e, finalmente, a análise de presença, ou ausência, de informação advinda dos padrões de preços. Como ilustração, são analisadas séries de diversos ativos do mercado financeiro mundial. A nossa investigação verifica a existência de conteúdo informativo estatisticamente significante em dois dos três padrões usualmente identificados na análise técnica, a saber: triângulos retângulos e head & shoulders. / [en] Technical analysis or charting aims on visually identifying geometrical patterns in price charts in order to anticipate price trends. This dissertation revisits the issue of technical analysis statistical validation, which has been tackled in the literature without taking care of the presence of heterogeneity and statistical dependence in the analyzed data - agglutinated return time series from many distinct securities. The main purpose of this study is to address the first cited problem by suggesting a methodology to homogenize the securities according to the probability distributions of their return series. The general steps of the methodology go through the identification of the data generating stochastic processes for the security returns, the clustering of similar securities and, finally, the analysis of the presence, or absence, of informational content coming from those price patterns. We illustrate the proposed methodology with several financial securities of the global market. Our investigation shows that there is a statistically significant informational content in two out of the three common patterns usually found through technical analysis, namely: triangles, rectangle and head & shoulders.

In security markets, the stock price movements are closely linked to the market information. For example, the subprime mortgage triggered a global financial crisis in 2007. Drops occurred in virtually every stock market in the world. After the Federal Reserve took several steps to address the crisis, the stock markets have been gradually stable. Reaction of the traders to the arrival information results in different patterns of the stock price movements. Thus pattern matching is an important subject in future movement prediction, rule discovery and computer aided diagnosis. In this research, we propose a pattern matching procedure to seize the similar stock price movements of two listed companies during one day. First, the algorithm of searching the longest common subsequence is introduced to sieve out the time intervals where the two listed companies have the same integrated volatility levels and price rise/drop trends. Next we transform the raw price data in the found matching time periods to the Bollinger Band Percent data, then use the power spectrum to extract low frequency components. Adjusted Pearson chi-squared tests are performed to analyze the similarity of the price movement patterns in these periods. We perform the study by simulation investigation first, then apply the procedure to empirical analysis of high frequency transaction data of NYSE.

This diploma thesis follows my bachelor thesis in which the mother slang was described. This diploma thesis is aimed at the performance of the mother speech research, i.e. the use of specific expressions and language resources used by mothers of small children in Internet discussions in relevant forums or web pages. The diploma thesis aims at creating a questionnaire and establishing five hypotheses. The first part of the thesis describes the methodology of this research, in the following part there are presented the data obtained by the questionnaire survey. The hypotheses are verified in the following section, and the hypothesis testing procedure is described here. The appendix includes the questionnaire and a table of critical values that specifies the data that are needed for verifying hypotheses.

The diploma thesis deals with the motivation factors of a rightful tax return. The aim of the thesis was to identify influence of attitude, subjective norms and behavioural control on a truthfulness of a taxpayer when filling in the tax return. The first part of the thesis is aimed on definition of a tax evasion. Furthermore, this part deals with the causes of tax evasions as well as with ethical point of view on tax evasions in general. The second part of the thesis deals with the indicators of extent and evolution of tax evasions in the Czech Republic and in the European Union. The indicators of tax evasions are the following: shadow economy, tax gap of VAT, tax quota, corruption index and frequency of tax control. The third part includes the results of the questionnaire survey that was realised among the Czech entrepreneurs. The results show the cases of tax evasions that the entrepreneurs may have consider as rightful. Thereafter, using the chi-squared test, the analysis examined whether the attitude of the entrepreneurs towards the tax evasions is influenced by the factors as company seat, annual turnover or number of employees. In several cases, the research confirmed an existence of dependence between attitude of entrepreneurs towards tax evasions and the factors stated above.

This degree project aims to explore the subject of forecasting, which is an ongoing and much alive debate within economics and finance. Within the forecasting field the available research is vast and even if restricted to real estate, which is the main focus of this paper, the available material is comprehensive. A large fraction of published research concerning the subject of real estate forecasting consists of post mortem studies, with econometric models trying to replicate historical trends with the help of available micro and macro data. This branch within the field of forecasting seems to advance and progress with help of refined econometric models. This paper, on the other hand, rather examines the fundamentals behind forecasting and why forecasting can be a difficult task in general. This is shown with an examination of the accuracy of 160 unique forecasts within the field of real estate. To evaluate the accuracy and predictability from different perspectives we state three main null hypotheses: 1. Correct forecasts and the direction of the predictions are independent variables. 2. Correct forecasts and the examined consultants are independent variables. 3. Correct forecasts and the examined cities are independent variables. 4 The observed frequencies for Hypothesis 1 indicate that upward predictions seem to be easier to predict than downward predictions. This is however not supported by the statistical tests. The observed frequencies for Hypothesis 2 clearly indicate that one consultant is a superior forecaster than compared to the other consultants. The statistical tests confirm this. The observed frequencies for Hypothesis 3 indicate no signs of dependence for the variables. The statistical tests confirm this. / Detta examensarbete ämnar att utforska ämnesområdet kring prognoser och prognosmakande, vilket är en högst levande debatt inom ekonomi och finans. Inom detta område är tillgänglig forskning mycket omfattande och även om materialet begränsas till fastighetsmarknaden, som är huvudspåret i denna uppsats, är mängden information ansenlig. En stor andel av publicerad forskning som berör prognoser av fastighetsmarkanden består ofta av studier av typen "post mortem", där man med ekonometriska modeller försöker efterlikna tidigare historiska trender med hjälp av tillgänglig mikro- eller makrodata. Denna gren av forskningen tycks vinna mark och fortsätter att utvecklas med hjälp av allt mer avancerade ekonometriska modeller. Denna studie fokuserar däremot snarare på de fundamentala elementen av prognosmakande och varför detta ibland kan vara en problematisk uppgift. Detta visas med hjälp av en undersökning gällande utfallet och träffsäkerheten av 160 unika prognoser på fastighetsmarknaden. 7 För att utvärdera träffsäkerheten hos prognoserna sätts tre olika nollhypoteser upp: 1. Korrekt prognos och riktning av prognos är oberoende variabler. 2. Korrekt prognos och konsult är oberoende variabler. 3. Korrekt prognos och undersökta städer är oberoende variabler. De observerade frekvenserna för Hypotes 1 indikerar att uppåtgående prognoser är enklare att förutspå än övriga prognoser. Detta kan dock inte stödjas av de statistiska testerna. De observerade frekvenserna för Hypotes 2 indikerar tydligt att en konsult är en överlägsen prognosmakare än övriga konsulter. Detta stöds av de statistiska testerna. De observerade frekvenserna för Hypotes 3 indikerar inget samband av beroende mellan variablerna. Detta kan dock inte stödjas av de statistiska testerna.

The first chapter covers the basics of the Internet as well as the strenghts and weaknesses of online shopping and data collection. The second chapter describes the decision-making process of the consumer along with possibilities of communications with customers and the differences between the bricks-and-mortar and the online customers. The third chapter provides research and results evaluation methods. The fourth chapter describes the selected search portals that help customers with the choice where to shop. The last chapter is devoted to the results of quantitative and qualitative research together with the recommendation of elements that an online store should include.