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Autocorrelated residuals of robust regression
Kalina, Jan
The work is devoted to the Durbin-Watson test for robust linear regression methods. First we explain consequences of the autocorrelation of residuals on estimating regression parameters. We propose an asymptotic version of the Durbin-Watson test for regression quantiles and trimmed least squares and derive an asymptotic approximation to the exact null distribution of the test statistic, exploiting the asymptotic representation for both regression estimators. Further, we consider the least weighted squares estimator, which is a highly robust estimator based on the idea to down-weight less reliable observations. We compare various versions of the Durbin-Watson test for the least weighted squares estimator. The asymptotic test is derived using two versions of the asymptotic representation. Finally, we investigate a weighted Durbin-Watson test using the weights determined by the least weighted squares estimator. The exact test is described and also an asymptotic approximation to the distribution of the weighted statistic under the null hypothesis is obtained.
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Using data mining to manage an enterprise.
Prášil, Zdeněk ; Pour, Jan (advisor) ; Novotný, Ota (referee)
The thesis is focused on data mining and its use in management of an enterprise. The thesis is structured into theoretical and practical part. Aim of the theoretical part was to find out: 1/ the most used methods of the data mining, 2/ typical application areas, 3/ typical problems solved in the application areas. Aim of the practical part was: 1/ to demonstrate use of the data mining in small Czech e-shop for understanding of the structure of the sale data, 2/ to demonstrate, how the data mining analysis can help to increase marketing results. In my analyses of the literature data I found decision trees, linear and logistic regression, neural network, segmentation methods and association rules are the most used methods of the data mining analysis. CRM and marketing, financial institutions, insurance and telecommunication companies, retail trade and production are the application areas using the data mining the most. The specific tasks of the data mining focus on relationships between marketing sales and customers to make better business. In the analysis of the e-shop data I revealed the types of goods which are buying together. Based on this fact I proposed that the strategy supporting this type of shopping is crucial for the business success. As a conclusion I proved the data mining is methods appropriate also for the small e-shop and have capacity to improve its marketing strategy.
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Applied quantitative methods of Austrian Business Cycle Theory
Kaláb, Jiří ; Svoboda, Miroslav (advisor) ; Janíčko, Martin (referee)
This paper analyzes the Austrian theory of business cycles. This theory describes the reasons that cause cyclical fluctuations in economic activity. Its foundations are built on the Austrian theory of capital. The main goal of this paper is to identify these reasons and construct a model based on them. This model attempts to capture the effect of explanatory variables on the structure of production according to Hayek's triangle. This is based on a sample of monthly U.S. data from the period 01/01/1977 to 04/01/2011. Data were tested using a linear regression model. Output from the model confirmed some of the variables as consistent with the Austrian theory of business cycles. However, there are many problems associated with applying this econometric model to the theory, whose leaders consistently opposed the introduction of mathematical methods in economic science.
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On Heteroscedasticity in Robust Regression
Kalina, Jan
This work studies the phenomenon of heteroscedasticity and its consequences for various methods of linear regression, including the least squares, least weighted squares and regression quantiles. We focus on hypothesis tests for these regression methods. The new approach consists in deriving asymptotic heteroscedasticity tests for robust regression, which are asymptotically equivalent to standard tests computed for the least squares regression. One approach to modeling heteroscedasticity assumes a prior knowledge or specific model for the variability of random regression errors. Another (and more general) approach does not assume a specific form of heteroscedasticity. The paper also describes heteroscedastic regression, which is a tool to incorporate heteroscedasticity to the model. This allows us to define the heteroscedastic least weighted squares regression.
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Forecast of the Future Development of the Current Business Crisis Using Tools of the Austrian School of Economics
Sehnalová, Tereza ; Svoboda, Miroslav (advisor) ; Mirvald, Michal (referee)
This paper is based on the theoretical framework given by the Austrian Business Cycle Theory. This theory explains clearly the causes, process and consequences of trade cycles that are inevitable parts of modern economies. Based on this framework, there was built a model trying to illustrate the impact of indicators standing behind the origin of business cycles on production structure of the USA examined on monthly data from years 1984 to 2009. The results of this model are conformable with predictions given by the Austrian Business Cycle Theory. Despite this, it is not possible to predict the future development of the US economy till the end of 2010 using this model, due to many problems that minimize relevance of such forecast. Nevertheless, it is possible to make prediction using the theory explained by the Austrian school of economics.
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The structure of household expenditure with regard to their income situation
Babáková, Andrea ; Bína, Vladislav (advisor) ; Bartošová, Jitka (referee)
Presented thesis is focused on searching for differences and investigating dependences between costs and revenues of households, mainly the housing expenditure are emphasized. The data were extracted from survey made by Czech Statistics Office, especially from sample survey about revenues and living conditions of households called "Životní podmínky 2005". The data are analyzed by means of linear regression and analysis of variance. The above mentioned statistical methods are used to investigate the level of dependence between incomes and housing costs with regard to various factors e.g. size and type of municipality or the type of house in which the particular household is living. The obtained results display slightly growing dependence between incomes and revenues. Furthermore a small survey of the particular households was made on which the selected linear regression model (obtained by the analysis of ČSÚ data) was applied. The comparison of both surveys showed rather insignificant differences.
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