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Bayesian modeling of market price using autoregression model
Šindelář, Jan
1 Bayesian modeling of market price using autoregression model 1Šindelář Jan Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Miroslav Kárný, DrSc. Abstract: In the thesis we present a novel solution of Bayesian filtering in autoregression model with Laplace distributed innovations. Estimation of regression models with lep- tokurtically distributed innovations has been studied before in a Bayesian framework [2], [1]. Compared to previously conducted studies, the method described in this article leads to an exact solution for density specifying the posterior distribution of parameters. Such a solution was previously known only for a very limited class of innovation distributions. In the text an algorithm leading to an effective solution of the problem is also proposed. The algorithm is slower than the one for the classical setup, but due to increasing com- putational power and stronger support of parallel computing, it can be executed in a reasonable time for models, where the number of parameters isn't very high. Keywords: Bayesian, Autoregression, Optimal Trading, Time Series References [1] P. Congdon. Bayesian statistical modelling. Wiley, 2006. [2] A. Zellner. Bayesian and Non-Bayesian analysis of the regression model with multivari- ate Student-t error term. Journal...
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Multivariate generalized autoregressive conditional heteroscedasticity models
Nováková, Martina ; Pešta, Michal (advisor) ; Maciak, Matúš (referee)
This master thesis deals with extension of the univariate GARCH model to multivari- ate models. We present individual models and deal with methods of their estimation. Then we describe some statistical tests for diagnosting the models. We have programmed in the statistical software R one of them - the Ling-Li test. Afterwards we apply selected models to real data of stock market index S&P 500, stock market index Russell 2000 and stocks of crude oil. For the GO-GARCH model, we compare all available estimation methods and show their differences. Then we compare the results of all models with each other and also with univariate models in terms of estimates of conditional variances, estimates of conditional correlations and also in terms of computational complexity. 1
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A correction of the local incidence angle of SAR data: a land cover specific approach for time series analysis
Paluba, Daniel ; Štych, Přemysl (advisor) ; Mouratidis, Antonios (referee)
To ensure the highest possible temporal resolution of SAR data, it is necessary to use all the available acquisition orbits and paths of a selected area. This can be a challenge in a mountainous terrain, where the side-looking geometry of space-borne SAR satellites in combination with different slope and aspect angles of terrain can strongly affect the backscatter intensity. These errors/noises caused by terrain need to be eliminated. Although there have been methods described in the literature that address this problem, none of these methods is prepared for operable and easily accessible time series analysis in the mountainous areas. This study deals with a land cover-specific local incidence angle (LIA) correction method for time-series analysis of forests in mountainous areas. The methodology is based on the use of a linear relationship between backscatter and LIA, which is calculated for each image separately. Using the combination of CORINE and Hansen Global Forest databases, a wide range of different LIAs for a specific forest type can be generated for each individual image. The algorithm is prepared and tested in cloud-based platform Google Earth Engine (GEE) using Sentinel-1 open access data, SRTM digital elevation model, and CORINE and Hansen Global Forest databases. The method was tested...
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Evaluation of forest vegetation based on time series of remote sensing data
Laštovička, Josef ; Štych, Přemysl (advisor) ; Brom, Jakub (referee) ; Bucha, Tomáš (referee)
Příloha k disertační práci: Abstrakt v AJ (Mgr. Josef Laštovička) Abstract This dissertation thesis deals with the study of forest ecosystems in the central Europe with the time series of multispectral optical satellite data. These forest ecosystems have been influenced by biotic and abiotic disturbances for the last decade. The time series of the satellite data with high spatial resolution allow the detection and analysis of forest disturbances. This thesis is mainly focused primally on free available Landsat and Sentinel-2 data, these two data types were compared. From methods, the difference time series analyses / algorithms were used. The whole thesis can be divided into two main parts. The first one analyses usability of classifiers for detection of forest ecosystems with per-pixel and sub-pixel methods. Specifically, the Neural Network, the Support Vector Machine and the Maximum Likelihood per-pixel classifiers were used and compared for different types of data (for data with high spatial resolution - Landsat or Sentinel-2; very high spatial resolution - WorldView-2) and for classification of protected forest areas. The Support Vector Machine were selected as the most suitable method for forest classifications (with most accurate outputs) from the list of selected per-pixel classifiers. Also, Spectral...
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Anomaly detection for stock market trading data
Fusková, Martina ; Kofroň, Jan (advisor) ; Kliber, Filip (referee)
Stock trading is a very complex topic that involves a lot of challenging problems. One of these problems is anomaly detection in trading flow. Real-time anomaly detection in time series is a very complicated task and thus this issue is still open. The aim of this thesis is to research various models and algorithms that can be used for this task and try to find the most fitting ones. We develop models that detect anomalies based on the density properties of the data as well as statistical models and neural networks that detect anomalies based on the comparison of predicted data and actual data. As a result we propose models that can be further researched and used in real-time environment.
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Probability forecast in exponential smoothing models
Viskupová, Barbora ; Hudecová, Šárka (advisor) ; Cipra, Tomáš (referee)
This thesis deals with the use of statistical state space models of exponential smooth- ing for estimating the conditional probability distribution of future values of time series. This knowledge allows calculation of interval predictions, not only point forecasts. Meth- ods of exponential smoothing are described and set into the context of state space models. Analytical and simulation methods used in the calculation of interval predictions are presented, in particular simulations based on assumption of normality, bootstrap method or estimated parametric model. The methods are applied to simulated as well as real data and their results are compared. 1
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Analysis of economic data using statistical methods
Grigoryeva, Ekaterina ; Novotná, Veronika (referee) ; Michalíková, Eva (advisor)
This bachelor's work deals with the assessment of the economic indicators of Samsung Electronics Czech and Slovak, s.r.o." using statistical and financial analysis methods. A quality assessment of the operation of the selected business is carried out in the thesis, the findings of the draft measures should improve its economic situation. Methods and tools for analyzing the business will be discussed both theoretically and practically. The conclusion of the thesis will give a full overview of the financial situation of the business.
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Assessment of Selected Indicators of a Company Using Statistical Methods
Novotný, Martin ; Přenosil, Jan (referee) ; Doubravský, Karel (advisor)
The bachelor thesis is focused on the assessment of the financial development of the company using time series and evaluation of financial indicators for the period 2012 to 2018. The bachelor thesis is divided into a theoretical part, which describes the financial analysis; regression analysis and time series from a theoretical point of view, a practical part that presents the company and analyzes individual financial indicators based on accounting terms. With the help of statistical indicators, further possible development of the analyzed indicators is determined, as well as proposals for improving the financial situation of the company, which is described in the last part of the bachelor's thesis.
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