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Robust Estimator of Persistence in Financial Time Series
Jeřábek, Jakub ; Hanzák, Tomáš (referee) ; Vošvrda, Miloslav (advisor)
The goal of this thesis is to develop a novel robust log-periodogram regression method to detect the presence of long memory in time series. By the use of the Least Trimmed Squares regression we obtain an estimator that is less sensitive to outliers and leverage points, which is highly desirable particularly because the Periodogram estimator itself is prone to such inhomogeneities. In a Monte Carlo study, the new estimator provides smaller bias than the classical Least Squares log-Periodogram estimator. On the other hand the variability of estimation is increased. The proposed estimator is compared to existing long memory estimators on a case study of international currency exchange rates.
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Dynamic analysis of portfolio by means of Kalman filter
Králová, Dana ; Hanzák, Tomáš (referee) ; Cipra, Tomáš (advisor)
The aim of the presented work is to introduce the new method of dynamic analysis of portfolio which estimates the composition of portfolio on the base of its returns. In the work, we describe the theory of Kalman filter and state space models. We mention examples of application of Kalman filter and demonstrate the work with econometric software EViews in the field of state space models on this examples. We deal with selected aspects from the portfolio theory. We present the older method of analysis of portfolio which uses the regression model and we draw attention to its essential lack. We deal, in more details, with the method of dynamic analysis of portfolio which is based on the state space models and which removes the lack of the older method. We also study the modification of this method for hedge funds. In the end, we apply the method of dynamic analysis of portfolio on the real data of two Czech investment funds and so we verify the quality of the model.
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Decomposition methods for time series with irregular observations
Hanzák, Tomáš ; Prášková, Zuzana (referee) ; Cipra, Tomáš (advisor)
This work deals with extensions of classical exponential smoothing type methods for univariate time series with irregular observations. Extensions of simple exponential smoothing, Holt method, Holt-Winters method and double exponential smoothing which have been developed in past are presented. An alternative method to Wright's modification of simple exponential smoothing for irregular data, based on the corresponding ARIMA process, is suggested. Exponential smoothing of order m for irregular data as a generalization of simple and double exponential smoothing is derived. A similar method using a DLS (discounted least squares) estimation of polynomial trend of order m is derived as well. In all cases the recursive character of these methods is preserved making them easy to implement and high computationally effective. A program in which most of the methods presented here are available is a part of the work. Some numerical examples of their application are also included.
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