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Detection of causality in time series using extreme values
Bodík, Juraj ; Pawlas, Zbyněk (advisor) ; Komárek, Arnošt (referee)
Juraj Bodík Abstract This thesis is dealing with the following problem: Let us have two stationary time series with heavy- tailed marginal distributions. We want to detect whether they have a causal relation, i.e. if a change in one of them causes a change in the other. The question of distinguishing between causality and correlation is essential in many different science fields. Usual methods for causality detection are not well suited if the causal mechanisms only manifest themselves in extremes. In this thesis, we propose a new method that can help us in such a nontraditional case distinguish between correlation and causality. We define the so-called causal tail coefficient for time series, which, under some assumptions, correctly detects the asymmetrical causal relations between different time series. We will rigorously prove this claim, and we also propose a method on how to statistically estimate the causal tail coefficient from a finite number of data. The advantage is that this method works even if nonlinear relations and common ancestors are present. Moreover, we will mention how our method can help detect a time delay between the two time series. We will show how our method performs on some simulations. Finally, we will show on a real dataset how this method works, discussing a cause of...
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Geometric approach to the estimation of scatter
Bodík, Juraj ; Nagy, Stanislav (advisor) ; Antoch, Jaromír (referee)
In this thesis we describe improved methods of estimating mean and scatter from multivariate data. As we know, the sample mean and the sample variance matrix are non-robust estimators, which means that even a small amount of measurement errors can seriously affect the resulting estimate. We can deal with that problem using MCD estimator (minimum covariance determinant), that finds a sample variance matrix only from a selection of data, specifically those with the smallest determinant of this matrix. This estimator can be also very helpful in outlier detection, which is used in many applications. Moreover, we will introduce the MVE estimator (minimum volume ellipsoid). We will discuss some of the properties and compare these two estimators.
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