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Methods of dynamical analysis of portfolio composition
Meňhartová, Ivana ; Hanzák, Tomáš (advisor) ; Cipra, Tomáš (referee)
Title: Methods of dynamical analysis of portfolio composition Author: Ivana Meňhartová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomáš Hanzák, KPMS, MFF UK Abstract: In the presented thesis we study methods used for dynamic analysis of portfolio based on it's revenues. The thesis focuses on Kalman filter and local- ly weighted regression as two basic methods for dynamic analysis. It describes in detail theory for these methods as well as their utilization and it discusses their proper settings. Practical applications of both methods on artificial data and real data from Prague stock-exchange are presented. Using artificial data we demonstrate practical importance of Kalman filter's assumptions. Afterwards we introduce term multicolinearity as a possible complication to real data applicati- ons. At the end of the thesis we compare results and usage of both methods and we introduce possibility of enhancing Kalman filter by projection of estimations or by CUSUM tests (change detection tests). Keywords: Kalman filter, locally weighted regression, multicollinearity, CUSUM test
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Analysis and prediction of league games results
Šimsa, Filip ; Hanzák, Tomáš (advisor) ; Večeř, Jan (referee)
The thesis is devoted to an analysis of ice hockey matches results in the highest Czech league competition in seasons 1999/2000 to 2014/2015 and to prediction of the following matches. We describe and apply Kalman filter theory where forms of teams represent an unobservable state vector and results of matches serve as measurements. Goal differences are identified as a suitable transformation of a match result. They are used as a dependent variable in a linear regression to find significant predictors. For a prediction of a match result we construct an ordinal model with those predictors. By using generalized Gini coefficient, we compare a diversifica- tion power of this model with betting odds, which are offered by betting companies. At the end, we combine knowledge of odds before a match with other predictors to make a prediction model. This model is used to identify profitable bets. 1
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Some problems of exponential smoothing
Čurda, David ; Hanzák, Tomáš (advisor) ; Komárek, Arnošt (referee)
In this work the several exponential smoothing type methods are briefly described, which are often used to smoothing and forecasting in the time series. Selected problems, that occur in described methods, are presented and in some cases there are the suggestions to their solution, which should tend to more suitable smoothing or to the better forecasts. It's shown how the methods are applied on different data and how the forecasts differ from each other. In conclusion the quality of modifications is evaluated.
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Exponential smoothing
Mikulka, Jakub ; Hanzák, Tomáš (advisor) ; Cipra, Tomáš (referee)
Nazev prace: Exponencialnivyrovnavani Autor: Jakub Mikulka Katedra: Katedra pravdepodobnosti a matematicke statistiky Vedouci bakalarske prace: Mgr. Tomas Hanzak e-mail vedouciho:hanzak@karlin.mff.cuni.cz Abstrakt: Prace se zabyva dvema metodami exponencialniho vyrovnavani pro nesezonni casove rady s lokalne linearnim trendem: Holtove metode a dvojitemu exponencialmmu vyrovnani (Brownove metode). Je ukazano, ze Brownova metoda je specialnim pnpadem Holtovy metody. Dale je uveden vztah procesu ARIMA(0, 2, 2) a Holtovy metody. Hlavni casti prace je teoreticke odvozeni hodnoty MSE a autokorelacniho koeficientu pfedpovedmch chyb Q pri pouziti Holtovy metody pro vsechny kombinace jejfch vyrovnavacich konstant za predpokladu generovani rady procesem ARIMA(0, 2, 2} pro vsechny hodnoty jeho parametru. Odvozene teoreticke vzorce jsou aplikovany tez na Brownovu metodu. Odvozene vzorce jsou pomoci simulaci overeny a vyzkouseny na realnych casovych radach. Jsou formulovany prakticke zavery tykajici se obou metod. Klicova slova: autokorelacni koeficient predpovednich chyb, Holtova metoda, dvojite exponencialni vyrovnavani,MSE, vyrovnavaci konstanty Abstract Title: Exponential smoothing Author: Jakub Mikulka Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomas Hanzak...
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Methods for periodic and irregular time series
Hanzák, Tomáš
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity
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Analysis of weather effect on TV audience
Leová, Monika ; Arltová, Markéta (advisor) ; Hanzák, Tomáš (referee)
Diploma thesis analyzes the influence of weather on TV audience in the Czech Republic in 2012 to 2016 by using data of the Association of Television Organizations and meteorological data of the Czech Hydrometeorological Institute. The first part of the thesis deals with the phenomenon of TV ratings, discusses its importance for contemporary society and puts it in the frame of other leisure activities. Additionally, it introduces the current Czech TV market, electronic measurement of TV ratings, its main institutions and complementary research. The empirical part of the diploma thesis focuses on realization of the statistical analysis. Weather components (temperature, rain falls and cloudiness) that affect TV viewing have been identified by using a suitable regression model and their weight in the aggregate meteo factor have been determined. The final model, in addition to weather elements, takes into account calendar effects (day of the week, holidays, season) as well as interaction between weather and calendar effects. The model was applied to total TV audience as well as to selected groups of TV channels, to individual age categories, whole day, prime time and off time and also separately to so called guests TV audience.
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Methods for periodic and irregular time series
Hanzák, Tomáš ; Cipra, Tomáš (advisor) ; Arlt, Josef (referee) ; Prášková, Zuzana (referee)
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity
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Methods for periodic and irregular time series
Hanzák, Tomáš
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity
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Analysis and prediction of league games results
Šimsa, Filip ; Hanzák, Tomáš (advisor) ; Večeř, Jan (referee)
The thesis is devoted to an analysis of ice hockey matches results in the highest Czech league competition in seasons 1999/2000 to 2014/2015 and to prediction of the following matches. We describe and apply Kalman filter theory where forms of teams represent an unobservable state vector and results of matches serve as measurements. Goal differences are identified as a suitable transformation of a match result. They are used as a dependent variable in a linear regression to find significant predictors. For a prediction of a match result we construct an ordinal model with those predictors. By using generalized Gini coefficient, we compare a diversifica- tion power of this model with betting odds, which are offered by betting companies. At the end, we combine knowledge of odds before a match with other predictors to make a prediction model. This model is used to identify profitable bets. 1
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Regression trees
Masaila, Aleh ; Hanzák, Tomáš (advisor) ; Zvára, Karel (referee)
Title: Regression trees Author: Aleh Masaila Department: Department of Probability and Mathematical Statistics Supervisor: Mgr.Tomáš Hanzák Abstract: Although regression and classification trees are used for data analysis for several decades, they are still in the shadow of more traditional methods such as linear or logistic regression. This paper aims to describe a couple of the most famous regression trees and introduce a new direction in this area - a combination of regression trees and committee methods, so called the regression forests. There is a practical part of work where we try properties, strengths and weaknesses of the examined methods on real data sets. Keywords: regression tree, CART, MARS, regression forest, bagging, boosting, random forest 1
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