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Transition Periods and Long Memory Property
März, Jan ; Vácha, Lukáš (advisor) ; Polák, Petr (referee)
This thesis examines the relationship between the distribution of structural breaks within a data sample and the estimated parameter of long memory. We use Monte Carlo simulations to generate data from processes with specific values of parameters. Subsequently we join the data with various shifts to mean and examine how the estimates of the parameters vary from their true values. We have discovered that the overestimate of the long memory parameter is higher when the breaks are clustered together. It further increases when the signs of the shifts are positively correlated within the clusters while negative correlation reduces the bias. Our findings enable the improvement of robustness of estimators against the presence structural breaks. Powered by TCPDF (www.tcpdf.org)
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Modeling of Long Memory in Volatility Using Wavelets
Kraicová, Lucie ; Baruník, Jozef (advisor) ; Adam, Tomáš (referee)
ii Abstract This thesis focuses on one of the attractive topics of current financial literature, the application of wavelet-based methods in volatility modeling. It introduces a new, wavelet-based estimator (wavelet Whittle estimator) of a FIEGARCH model, ARCH- family model capturing long-memory and asymmetry in volatility, and studies its properties. Based on an extensive Monte Carlo experiment, both the behavior of the new estimator in various situations and its relative performance with respect to two more traditional estimators (maximum likelihood estimator and Fourier-based Whittle estimator) are assessed, along with practical aspects of its application. Possible solutions are proposed for most of the issues detected, including suggestion of a new specification of the estimator. This uses maximal overlap discrete wavelet transform instead of the traditionally used discrete wavelet transform, which should improve the estimator performance in all its applications, not only in the case of FIEGARCH model estimation. The thesis concludes that, after optimization of the estimation setup, the wavelet-based estimator may become an attractive robust alternative to the traditional methods.
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Three Essays on Electricity Markets
Luňáčková, Petra ; Janda, Karel (advisor) ; Tashpulatov, Sherzod (referee) ; Knápek, Jaroslav (referee) ; Möst, Dominik (referee)
DISSERTATION - Abstract in English Three Essays on Electricity Markets Author: PhDr. Petra Luňáčková Academic Year: 2017/2018 This thesis consists of three papers that share the main theme - energy. The articles introduce characteristics and behavior of electricity focusing on its unique properties. The dissertation aims at the Czech electricity market and analyzes also highly discussed solar power plants. The first article studies long term memory properties of electricity spot prices through the detrended fluctuation analysis, as electricity prices are dominated by cycles. We conclude that Czech electricity prices are strongly mean reverting yet non-stationary. The second part of the dissertation investigates possible asymmetry in the gas - oil prices adjustment. Oil prices determine the price of electricity during the times of peak demand, as the reaction of power plants fueled by oil is quick but marginal costs are high. We chose the gasoline - crude oil relationship known as "rockets and feathers" effect and offer two new tests to analyze such type of relationship as we believe that error correction model is not the most suitable tool. Analyzing international dataset we do not find statistically significant asymmetry. The third study assesses the impact of renewable energy sources, solar plants in...
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Forecasting in futures markets: Front, back and rolling contracts
Badáňová, Martina ; Krištoufek, Ladislav (advisor) ; Adam, Tomáš (referee)
In the thesis we analyze sixteen commodity futures markets belonging to four families (energy type, grains, metals and other agricultural commodities) utilizing futures prices of front, back and roll futures contracts. As the tests for cointegration between front and back futures prices give us contradictory results we concentrate on roll contracts defined as the difference between front and back commodity futures contracts. We found that all commodity roll futures except natural gas and wheat futures exhibit long memory, which is usually connected with the fractal market hypothesis. Further, we employ specific ARMA and ARFIMA models and rolling window one-day-ahead technique to predict roll futures contract prices. Based on analysis of relation between resulting predictability and liquidity of roll futures contracts we concluded that lowest predictability is linked with the lowest liquidity among all commodities except metals and found evidence that predictability is positively dependent on liquidity among all commodities except metals, lumber, soybean oil and soybeans. The revealed dependence is strongest for energy type commodities. The relations and dependencies on the commodity futures markets are of high importance for all market participants such as hedge managers, investors, speculators and also for...
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Transition Periods and Long Memory Property
März, Jan ; Vácha, Lukáš (advisor) ; Polák, Petr (referee)
This thesis examines the relationship between the distribution of structural breaks within a data sample and the estimated parameter of long memory. We use Monte Carlo simulations to generate data from processes with specific values of parameters. Subsequently we join the data with various shifts to mean and examine how the estimates of the parameters vary from their true values. We have discovered that the overestimate of the long memory parameter is higher when the breaks are clustered together. It further increases when the signs of the shifts are positively correlated within the clusters while negative correlation reduces the bias. Our findings enable the improvement of robustness of estimators against the presence structural breaks. Powered by TCPDF (www.tcpdf.org)
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Multifractal analysis of petrol and diesel prices in the Czech Republic
Baletka, Martin ; Krištoufek, Ladislav (advisor) ; Gregor, Martin (referee)
This thesis examines scaling properties of petrol and diesel prices in the Czech Republic and a crude oil price over the period from January 2004 to February 2013. Using generalised Hurst exponent and multifractal detrended fluctuation analysis techniques we find out that crude oil market is efficient, do not contain long memory and the returns exhibit monofractal behaviour. On the other hand, petrol and diesel markets in the Czech Republic are not efficient, because their returns contain long-range dependence in autocorrelations and exhibit multifractal behaviour caused mostly by fat-tailed distribution. Thus, fuels can be modelled by complex methods like Markov switching multifractal model. JEL Classification C15, C16, C46 Keywords petrol, diesel, crude oil, long memory, multifrac- tality, GHE, MF-DFA Author's e-mail martin.baletka@ies-prague.org Supervisor's e-mail kristoufek@ies-prague.org Abstrakt Tato práce zkoumá škálování cen benzínu a motorové nafty v České repub- lice a ceny ropy na datech v období od ledna 2004 do února 2013. Použitím metod zobecněného Hurstova exponentu a multifraktální detrendované fluk- tuační analýzy jsme zjistili, že trh s ropou je efektivní, bez přítomnosti dlouhé paměti v autokorelacích a výnosy na trhu s ropou vykazují monofraktální...
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Modeling of Long Memory in Volatility Using Wavelets
Kraicová, Lucie ; Baruník, Jozef (advisor) ; Adam, Tomáš (referee)
ii Abstract This thesis focuses on one of the attractive topics of current financial literature, the application of wavelet-based methods in volatility modeling. It introduces a new, wavelet-based estimator (wavelet Whittle estimator) of a FIEGARCH model, ARCH- family model capturing long-memory and asymmetry in volatility, and studies its properties. Based on an extensive Monte Carlo experiment, both the behavior of the new estimator in various situations and its relative performance with respect to two more traditional estimators (maximum likelihood estimator and Fourier-based Whittle estimator) are assessed, along with practical aspects of its application. Possible solutions are proposed for most of the issues detected, including suggestion of a new specification of the estimator. This uses maximal overlap discrete wavelet transform instead of the traditionally used discrete wavelet transform, which should improve the estimator performance in all its applications, not only in the case of FIEGARCH model estimation. The thesis concludes that, after optimization of the estimation setup, the wavelet-based estimator may become an attractive robust alternative to the traditional methods.
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Backtesting of Different Scaling Rules for Value at Risk in the Basel Context
Klečka, Adam ; Krištoufek, Ladislav (advisor) ; Avdulaj, Krenar (referee)
1 Abstract There is a discrepancy between two important horizon for Value at Risk modelling in the Basel context. We take 10-day values for determining the regulatory capital but we consider 1-day models for backtesting. The main objective of this thesis is to examine the suitability of the currently used Square Root of Time rule for Value at Risk scaling. We compare its performance with the method utilizing Hurst exponent. Our analysis is performed for both the normal and stable distribution. We conclude that the normality assumption and the Square Root of Time rule prevail under the regulatory parameters. The results of the Hurst exponent method are not favourable under normality. On the other hand, the performance for the stable distribution is quite satisfactory under non-Basel parameters and the Hurst exponent complements this distribution very well. Therefore, the use of stable distribution and the Hurst exponent method is justified when dealing with complex non-linear instruments, during turbulent periods, or for general non-Basel setting. In general however, our results are strongly data-dependent and further evidence is needed for any conclusive implications. JEL Classification G21, G28, C58, G32, C14, G18 Keywords value at risk, backtesting, volatility scaling, Basel II, stable distribution, Hurst...
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Multifractal Analysis of Stock Market Prices
Čechová, Kristýna ; Krištoufek, Ladislav (advisor) ; Vošvrda, Miloslav (referee)
The aim of this thesis is to provide an empirical evidence of multifractality in financial time series and to discuss the relevance of this concept for the current financial theory. We have applied two methods, the Multifractal Detrended Fluctuation analysis and the Generalized Hurst exponent method, on components of the Dow Jones Industrial Average. We analyzed daily data of 30 companies traded on U.S. stock markets from 2002 to 2012. We present results supporting presence of multiscaling in open-close returns. Contrary to published literature, we were not able to find any significant multiscaling in volatility. Moreover based on our analysis, multiscaling is not present in standardized returns and as multifractality requires relatively complicated models, this is our most valuable result. 1
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Range-based volatility estimation and forecasting
Benčík, Daniel ; Baruník, Jozef (advisor) ; Krištoufek, Ladislav (referee)
In this thesis, we analyze new possibilities in predicting daily ranges, i.e. the differences between daily high and low prices. The main focus of our work lies in investigating how models commonly used for daily ranges modeling can be enhanced to provide better forecasts. In this respect, we explore the added benefit of using more efficient volatility measures as predictors of daily ranges. Volatility measures considered in this work include realized measures of variance (realized range, realized variance) and range-based volatility measures (Parkinson, Garman & Klass, Rogers & Satchell, etc). As a subtask, we empirically assess efficiency gains in volatility estimation when using range-based estimators as opposed to simple daily ranges. As another venue of research in this work, we analyze the added benefit of slicing the trading day into different sessions based on trading activity (e.g. Asian, European and American session). In this setting we analyze whether whole-day volatility measures reliably aggregate information coming from all trading sessions. We are led by intuition that different sessions exhibit significantly different characteristics due to different order book thicknesses and trading activity in general. Thus these sessions are expected to provide valuable information concealed in...
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