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Time series dynamic factor analysis
Slávik, Ľuboš ; Michálek, Jaroslav (oponent) ; Hübnerová, Zuzana (vedoucí práce)
This thesis studies a novel approach to time series clustering based on a dynamic factor model. Dynamic factor model is a dimension reduction technique enhancing classical factor analysis by a requirement of an autocorrelation structure of the latent factors. Parameters of the model are estimated via EM algorithm employing Kalman filtering and smoothing and necessary restrictions are placed on the model, so the model becomes identifiable. After describing the theoretical concept of the approach, the dynamic factor model is applied to the real observed time series and the work discusses its behaviour and properties on one-month meteorological data of fire weather index at 108 fire stations located in British Columbia. The procedure of the model estimates a loadings matrix of the model with a corresponding small number of latent factors and a variance-covariance matrix of the modeled time series. The thesis applies k-means clustering to the resulted loadings matrix and provides a division of the stations into clusters based on the reduced dimensionality of the original data. With the estimated cluster means and the latent factors, it is possible to obtain particular mean trends for each cluster. Then, the achieved clusters are compared with the results obtained for the same set of stations but within a different month to assess the stability of the clustering. The work discusses the effect of varimax rotation on the loadings matrix as well. Moreover, the thesis suggests a method for detecting possible time series outliers based on the estimated variance-covariance matrix of the model and discusses the effect of outliers on the estimated model.
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Statistical analysis of laser spectroscopy measurements
Slávik, Ľuboš ; Bednář, Josef (oponent) ; Hübnerová, Zuzana (vedoucí práce)
The goal of this bachelor's thesis is to briefly describe Laser-induced breakdown spectroscopy method for analysis of elemental composition of studied samples. Outcomes of LIBS analysis (emission spectra) are further proceeded with mathematical methods of regression analysis. The goal is to find relations between measured chemical elements. These two methods are used for analysing real data based problem, that is to find specific relation between presence of uranium and hydrozirconium in a studied sample uranium-hosted sandstone.
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Time series dynamic factor analysis
Slávik, Ľuboš ; Michálek, Jaroslav (oponent) ; Hübnerová, Zuzana (vedoucí práce)
This thesis studies a novel approach to time series clustering based on a dynamic factor model. Dynamic factor model is a dimension reduction technique enhancing classical factor analysis by a requirement of an autocorrelation structure of the latent factors. Parameters of the model are estimated via EM algorithm employing Kalman filtering and smoothing and necessary restrictions are placed on the model, so the model becomes identifiable. After describing the theoretical concept of the approach, the dynamic factor model is applied to the real observed time series and the work discusses its behaviour and properties on one-month meteorological data of fire weather index at 108 fire stations located in British Columbia. The procedure of the model estimates a loadings matrix of the model with a corresponding small number of latent factors and a variance-covariance matrix of the modeled time series. The thesis applies k-means clustering to the resulted loadings matrix and provides a division of the stations into clusters based on the reduced dimensionality of the original data. With the estimated cluster means and the latent factors, it is possible to obtain particular mean trends for each cluster. Then, the achieved clusters are compared with the results obtained for the same set of stations but within a different month to assess the stability of the clustering. The work discusses the effect of varimax rotation on the loadings matrix as well. Moreover, the thesis suggests a method for detecting possible time series outliers based on the estimated variance-covariance matrix of the model and discusses the effect of outliers on the estimated model.
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Statistical analysis of laser spectroscopy measurements
Slávik, Ľuboš ; Bednář, Josef (oponent) ; Hübnerová, Zuzana (vedoucí práce)
The goal of this bachelor's thesis is to briefly describe Laser-induced breakdown spectroscopy method for analysis of elemental composition of studied samples. Outcomes of LIBS analysis (emission spectra) are further proceeded with mathematical methods of regression analysis. The goal is to find relations between measured chemical elements. These two methods are used for analysing real data based problem, that is to find specific relation between presence of uranium and hydrozirconium in a studied sample uranium-hosted sandstone.
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