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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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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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Linear and nonlinear autoregressive models for time series from economics and finance
Cvetković, Jelena ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This bachelor thesis deals with linear and nonlinear autoregressive models for time series from economics and finance. It consists of theoretical and practical part. In theoretical part, the reader acquaints with terms connected to random proces- ses; then autoregressive and threshold autoregressive time series are introduced, their general properties are derived, possible ways of forecasting are described and ways of parameters estimation are presented. Furthermore, test for threshold autoregression is introduced. The practical part is divided into simulation study, where the quality of estimations and the power of the test is examined on simu- lated time series, and into application on real data, where the acquired findings are utilized on time series of share prices of the company ČEZ. 1
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Econometric Modelling and Forecasting of Natural Gas Spot Prices
Kubišová, Barbora ; Hendrych, Radek (advisor) ; Hudecová, Šárka (referee)
The thesis deals with modeling and forecasting of natural gas spot prices, con- sumption of natural gas and average daily temperature. We assume that these three variables are influenced by each other, because as temperature decreases, consumption increases, which in turn increases the price with the increasing de- mand. Therefore, we propose to model these variables by vector autoregression. We compare this model with one-dimensional models where for each one we build a model from the ARMA-GARCH class. Models are estimated using historic va- lues and then designed models are used to simulate scenarios. Analysis of scenarios provides information to gas supply companies estimates of portfolio consumption and financial flows related to the purchase concerning natural gas. 1
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Econometric models of national economies
Hála, Petr ; Hendrych, Radek (advisor) ; Hurt, Jan (referee)
The present thesis deals with multiple econometric equations systems which might provide a useful insight into the national economy modelling. It takes into account possible pitfalls of common practices. It introduces the theory and estimation methods of multiple econometric equations systems. It also discusses the equality of savings and investment and the theory of money. Furthermore, it briefly analyses Klein's model I from a theoretical point of view and uses the three-step least squares method in order to estimate it. Partial modifications of this model are suggested and implemented. The quality of the competitive models is evaluated employing the predictive criterion. Consequently, the canonical NK DSGE model is derived and subjected to theoretical criticism. The thesis debates doubts on the relevance of the NK IS curve and argues that Lucas's critique is still valid. A generalized method of moments is used to implement the NK DSGE model. Finally, this model is briefly compared with Klein's model I.
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