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Wavelet-based Realized Variation and Covariation Theory
Baruník, Jozef ; Vošvrda, Miloslav (advisor) ; Kočenda, Evžen (referee) ; Di Matteo, Tiziana (referee) ; Veredas, David (referee)
English Abstract The study of volatility and covariation has become one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This dissertation contains a complete theory for realized variation and covariation estima- tion, generalizing current knowledge and taking the estimation into the time-frequency domain for the first time. The first part of the theory presents a wavelet-based realized variation theory, while the second part introduces its multivariate counterpart, a wavelet- based realized covariation theory. The results generalize the popular realized volatility framework by bringing robustness to noise as well as jumps and the ability to measure realized variation and covariation not only in the time domain, but also in the frequency domain. The theory is also tested in a numerical study of the small sample performance of the estimators and compared to other popular realized variation estimators under dif- ferent simulation settings with changing noise as well as jump level. The results reveal that our wavelet-based theory is able to estimate the realized measures with the greatest precision. Another notable contribution lies in the application of the presented theory. Our time-frequency estimators not only produce more efficient...
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Essays in Financial Econometrics
Avdulaj, Krenar ; Baruník, Jozef (advisor) ; Di Matteo, Tiziana (referee) ; Kočenda, Evžen (referee) ; Witzany, Jiří (referee)
vi Abstract Proper understanding of the dependence between assets is a crucial ingredient for a number of portfolio and risk management tasks. While the research in this area has been lively for decades, the recent financial crisis of 2007-2008 reminded us that we might not understand the dependence properly. This crisis served as catalyst for boosting the demand for models capturing the dependence structures. Reminded by this urgent call, literature is responding by moving to nonlinear de- pendence models resembling the dependence structures observed in the data. In my dissertation, I contribute to this surge with three papers in financial econo- metrics, focusing on nonlinear dependence in financial time series from different perspectives. I propose a new empirical model which allows capturing and forecasting the conditional time-varying joint distribution of the oil - stocks pair accurately. Em- ploying a recently proposed conditional diversification benefits measure that con- siders higher-order moments and nonlinear dependence from tail events, I docu- ment decreasing benefits from diversification over the past ten years. The diver- sification benefits implied by my empirical model are, moreover, strongly varied over time. These findings have important implications for asset allocation, as the benefits of...
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Long-range cross-correlations: Tests, estimators and applications
Krištoufek, Ladislav ; Vácha, Lukáš (advisor) ; Di Matteo, Tiziana (referee) ; Peng Liu, Rui (referee) ; Onali, Enrico (referee)
The motivation of this thesis is to provide a basic framework for treating long-range cross-correlated processes while keeping the methodology and as- sumptions as general as possible. Starting from the definition of long-range cross-correlated processes as jointly stationary processes with asymptotically power-law decaying cross-correlation function, we show that such definition implies a divergent at origin cross-power spectrum and power-law scaling of covariances of partial sums of the long-range cross-correlated processes. Chap- ter 2 describes these and other basic definitions and propositions together with necessary proofs. Chapter 3 then introduces several processes which possess long-range cross-correlated series properties. Apart from cases when the mem- ory parameter of the bivariate memory is a simple average of the parameters of the separate processes, we also introduce a new kind of process, which we call the mixed-correlated ARFIMA, which allows to control for both the bi- variate and univariate memory parameters. Chapter 4 deals with tests for a presence of long-range cross-correlations. We develop three new tests, and Monte-Carlo-simulation-based statistical power and size of the tests are com- pared. The newly introduced tests strongly surpass the already existing one. In Chapter 5,...
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Wavelet-based Realized Variation and Covariation Theory
Baruník, Jozef ; Vošvrda, Miloslav (advisor) ; Kočenda, Evžen (referee) ; Di Matteo, Tiziana (referee) ; Veredas, David (referee)
English Abstract The study of volatility and covariation has become one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This dissertation contains a complete theory for realized variation and covariation estima- tion, generalizing current knowledge and taking the estimation into the time-frequency domain for the first time. The first part of the theory presents a wavelet-based realized variation theory, while the second part introduces its multivariate counterpart, a wavelet- based realized covariation theory. The results generalize the popular realized volatility framework by bringing robustness to noise as well as jumps and the ability to measure realized variation and covariation not only in the time domain, but also in the frequency domain. The theory is also tested in a numerical study of the small sample performance of the estimators and compared to other popular realized variation estimators under dif- ferent simulation settings with changing noise as well as jump level. The results reveal that our wavelet-based theory is able to estimate the realized measures with the greatest precision. Another notable contribution lies in the application of the presented theory. Our time-frequency estimators not only produce more efficient...
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