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Tests for time series linearity
Melicherčík, Martin ; Prášková, Zuzana (advisor) ; Hendrych, Radek (referee)
Title: Testing for linearity in time series Author: Martin Melicherčík Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zuzana Prášková, CSc., Department of Probability and Mathematical Statistics Abstract: In the first part of the thesis, a necessary theoretical base from time series analysis is explained, which is consequently used to formulate several tests for linearity. According to variety of approaches the theory includes wide range of knowledge from correlation and spectral analysis and introduces some basic nonlinear models. In the second part, linearity tests are described, classified and compared both theoretically and practically on simulated data from several linear and nonlinear models. At the end, some scripts and hints in R language are introduced that could be used when applying tests to real data. Keywords: linear time series, bispectrum, testing for linearity, nonlinear models
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Principal components analysis and its applications
Dubová, Mária ; Hendrych, Radek (advisor) ; Prášková, Zuzana (referee)
In the present thesis, we deal with the principal components analy- sis. In the first of this text, we study different aspects of principals components, for instance, their derivation for a multidimensional random vector from general distribution or their calculation based on a covariance or correlation matrix. It is also important to choose the proper number of principal components for reducing the dimensionality of data in order to preserve most of information. Theoretical knowledge are illustrated with several examples. In the second part of the thesis, we focus on the value at risk. This term is defined in the text also with seve- ral usual formulas to calculate it. Then, we deal with a practical application of this concept and the principal component analysis. Concretely, we analyse the portfolio of some different interest rates to obtain the value at risk in some cases. 1
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Holt-Winters method with missing observations and its actuarial application
Gregor, Jiří ; Cipra, Tomáš (advisor) ; Hendrych, Radek (referee)
Title: Holt-Winters method with missing observations and its actuarial application Author: Jiří Gregor Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Tomáš Cipra, DrSc. Supervisor's department: Department of Probability and Mathematical Statistics Abstract: This thesis describes problematics of time series and its seasonal component. It shows different approaches to smoothing and prediction of time series. The main part of thesis is devoted to Holt-Winters method with missing observations and its actuarial application. Keywords: Time serie, smoothing, Holt-Winters method with missing observations 1
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Econometric systems of simultaneous equations in life insurance
Hendrych, Radek
Title: Econometric systems of simultaneous equations in life insurance Author: Radek Hendrych Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Tomáš Cipra, DrSc. Supervisor's e-mail address: cipra@karlin.mff.cuni.cz Abstract: In present work we deal with theoretical and practical issues related to econometric systems of (linear) simultaneous equations. In the first chapter we introduce to theoretical aspects of this problem. We devote considerable space to estimation procedures and comparisons of their properties, mention questions of identification, an inconsistency of OLS-estimates for the simultaneous modeling, tests of hypotheses specific to this area, dynamic systems and constructions of forecasts in models. In the second chapter we introduce selected basic concepts relevant to life insurance. In the third chapter we show the practical application of theoretical knowledge in the event of an econometric model of financial flows in the life insurance company operating on the Czech market. We compare ordinary estimation procedures (2SLS and 3SLS approach), perform some tests, which serve us to verify selected information on the studied model. We show the possibility of using residual bootstrap, including examples of use in the construction of confidence intervals....
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Linear volatility modeling in financial time series
Kollárová, Dominika ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
The aim of this master thesis is to introduce models belonging to ARCH(∞) representation where a time series volatility is modelled as a linear function of squared residuals. Specifically, the thesis deals with models IGARCH, FIGARCH and HYGARCH that are used to analyse, model and predict a development of financial time series. Definition and graphical illustration of individual models together with their application on real data, is supplemented by a simulation study of first-order FIGARCH model.
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Modern predictive methods for financial time series
Herrmann, Vojtěch ; Hendrych, Radek (advisor) ; Cipra, Tomáš (referee)
This thesis deals with comparing two approaches to modelling and predicting time series: a traditional one (the ARIMAX model) and a modern one (gradiently boosted decision trees within the framework of the XGBoost library). In the first part of the thesis we introduce the theoretical framework of supervised learning, the ARIMAX model and gradient boosting in the context of decision trees. In the second part we fit the ARIMAX and XGBoost models which both predict a specific time series, the daily volume of the S&P 500 index, which is a crucial task in many branches. After that we compare the results of the two approaches, we describe the advantages of the XGBoost model, which presumably lead to its better results in this specific simulation study and we show the importance of hyperparameter optimization. Afterwards, we compare the practicality of the methods, especially in regards to their computational demands. In the last part of the thesis, a hybrid model theory is derived and algorithms to get the optimal hybrid model are proposed. These algorithms are then used for the mentioned prediction problem. The optimal hybrid model combines ARIMAX and XGBoost models and performs better than each of the individual models on its own. 1
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Multivariate financial time series models in portfolio optimization
Bureček, Tomáš ; Hendrych, Radek (advisor) ; Prášková, Zuzana (referee)
This master thesis deals with the modeling of multivariate volatility in finan- cial time series. The aim of this work is to describe in detail selected approaches to modeling multivariate financial volatility, including verification of models, and then apply them in an empirical study of asset portfolio optimization. The results are compared with the classical approach of portfolio optimization theory based on unconditional moment estimates. The evaluation was based on four known op- timization problems, namely minimization of variance, Markowitz's model, ma- ximization of the Sharpe ratio and minimization of CVaR. The output portfolios were compared by using four metrics that reflect the returns and risks of the port- folios. The results demonstrated that employing the multivariate volatility models one obtains higher expected returns with less expected risk when comparing with the classical approach. 1
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Modelling Duration of Financial Transaction Data
Nácovský, Patrik ; Hendrych, Radek (advisor) ; Branda, Martin (referee)
This bachelor thesis deals with ACD (autoregressive conditional duration) model, which is used to estimate durations of time series of financial transaction data. First, duration and time series are defined formally as well as with the intuitive way. Next, model ACD itself is defined and its basic types, which are determined with distribution of its residuals. Then way to use this model for predictions is introduced. In the second part, steps for model identification, construction and revision are described. In the last part models EACD, WACD and GACD are constructed for real data. There are three data sets of thick data, which are Apple stocks, EUR/USD and gold. Data sets contain from 300 thousands to 600 thousands elements (one trading week).
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Backtesting Value-at-Risk: Comparison of selected approaches
Šedivý, Milan ; Hendrych, Radek (advisor) ; Hurt, Jan (referee)
This thesis focuses on the evaluation of different backtesting methods that are routinely applied to one of the most commonly used risk measure Value- at-Risk. The main goal of this thesis is to present approaches used to backtest Value-at-Risk (including an introduction to common methods associated with Value-at-Risk forecasting). These statistical evaluation methods are then applied to historical data from the years 2005 to 2010, during which we experienced two major financial crises. Afterwards, the output of our analysis is thoroughly discussed. 1
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