| Postdoctoral research | |
|---|---|
| Fitting Archimax copula to bivariate data in R | |
| PhD. study (Applied mathematics: Multivariate time-series analysis) | |
| 2007 | Advanced methods of time series modelling and their application in geodesy (Dissertation thesis) |
| 2006 | Multivariate logistic smooth transition autoregressive models |
| Fitting Archimedean copulas to bivariate geodetic observations | |
| 2005 | Modern multivariate approach to modelling... (Written part of dissertation exam) |
| Testing for common deterministic trends | |
| 2004 | Time-series modelling in the light of cointegration |
| Modelling point's position time series with respect to common trend | |
| Multivariate threshold autoregressive models | |
| Bc. a Ing. study (Geodesy and cartography; Global geodesy) | |
| 2003 | Least square spectral analysis (Diploma thesis) |
| 2002 | Computerization of geodetic calculations by means of programing languages |
| 2001 | Hardware and software for geoinformation systems |
Fitting Archimax copula to bivariate data in R | |
|---|---|
Abstract:Concept of Archimax copulas incorporates dependence function (known from EV copulas) into Archimedean class and thus allows for asymmetry. Here we propose some construction methods and implement fitting procedures in freely available environment for statistical computing and visualization, R.For more details, please redirect to:www.math.sk/wiki/bacigal |
|
|
| |
Advanced methods of time series modelling and their application in geodesy | |
Introduction:Many technical disciplines involved in civil engineering such as geology, geodesy, hydrology, statics of structures and others deal with geometric and physical quantities to figure out processes that influence our environment (both original and man-made). Supported by advancements and automation on the field of measuring instruments, monitoring becomes robust and effective, yet demanding more appropriate methods of processing. The most obvious geometric concern in geodesy is to determine a position of particular points in time-space. For the purpose, variety of techniques has been developed to precisely measure all the related mediating parameters, yet there is a special one popularity of which has rocketed up in recent times -- Global positioning system (GPS).Time series processing is the branch of statistics with relatively strong fan club, especially in the economic and financial applications, for which the majority of existing models and techniques has been developed so far. The most popular framework for modelling social-economic processes is autoregressive model and its various versions, which has long been applied to describe stationary phenomena. The idea of explaining the process by its past values has also been very useful for prediction. We use this approach as the groundwork in this thesis for introducing further extensions and developments, even as a contrast to completely different approach. That is the case we want to find relations between simultaneous values of particular variables in order to understand the interactions in the system of interest (society or nature). Obviously, one would get a lot more information by relating the values of variables at the same time point rather than relating it to its own past. The perfect example of modelling purely the relationships is the concept of copulas. However, parallel discussion of relations and individual dynamics makes great sense many times in practice. Therefore the thesis focuses on multivariate modelling which has much more capacities to describe real world than univariate approach. Application of models developed for clearly a different area and verification of its usefulness is one of the main purposes of our work. Another one is to bring modern methods, which are still evolving, closer to common practitioners in geodesy and other technical disciplines. The thesis is organised as follows. After stating our main goals, we continue with an overview of methods widely used for time series analysis assuming linearity. The concepts described there are to be the shoulders to stand on in the next two chapters, specifically when non-linearity or common features are expected. The fourth theoretical chapter introduces approach, that is new to time series modelling and disposes of completely different battery of tools, entirely focusing on intervariate relations. The description of existing methods in these four chapters is here and there supplemented by our own theoretical achievements and these are summarized in the Conclusion among practical results. In the fifth chapter the application to GPS observations is given to illustrate the theory and a brief description of accompanying algorithms is provided, which themselves find their place in appendix. Procedures in Mathematica 5.2:Appendix 1: Regime-switching models (237kB).nb.zipAppendix 2: Common trend and seasonal component (353kB).nb.zip Appendix 3: Functions utilised in appendices 1 and 2 ( 39kB).nb.zip Appendix 4: Fitting Archimedean copula (139kB).nb.zip |
Full paper:front matter (44kB).pdfchapter 1 (240kB).pdf chapter 2 (210kB).pdf chapter 3 (218kB).pdf chapter 4 (132kB).pdf chapter 5 (352kB).pdf back matter (65kB).pdf appendix 1 (167kB).pdf appendix 2 (126kB).pdf appendix 3 (179kB).pdf appendix 4 (152kB).pdf |
|
| |
Multivariate logistic smooth transition autoregressive models | |
Abstract:Regime-switching models and particularly the threshold autoregressive ones are used to process the data, which are nonlinear, or rather piecewise linear. Here we extend the multivariate TAR to LSTAR family of models, where the transition function between regimes is smooth, not jumpy. LSTAR stands for logistic smooth transition autoregressive. Application to geodetic data processing is given.Published:Bacigál, T.: Multivariate LSTAR in geodesy,- Proceedings of abstracts ISCAM 2006, April 7-8, 2006, Bratislava - Journal of Electrical Engineering, Vol. 57, No. 12/S, 2006 |
Presentation:ISCAM'06 ( 79kB).pdfFull paper:ISCAM'06 (176kB).pdf |
|
| |
Fitting Archimedean copulas to bivariate geodetic observations | |
Abstract:Copulas - the functions that link univariate marginals to their joint distribution function and thus capture solely the relationship among individual random variables - are being applied here to bivariate geodetic observations. The focus is put on three Archimedean families and their estimation procedures are outlined, namely nonparametric, semi-parametric approach and nonlinear least squares fit to empirical copula. Also a linear convex combination of two copulas is estimated to show one example of multi-parameter extension leading to real data fit improvement.Published:Bacigál, T.: Modelling Relationship Using Archimedean Copula: An Introduction to Experimental Study,- Proceedings of MAGIA 2005, November 28-30, 2005, Kočovce Bacigál, T.: Fitting Archimedean copulas to bivariate geodetic observations, - Proceedings of APLIMAT 2006, February 7-10, 2006, Bratislava - Abstracts of FSTA 2006, January 30 - February 3, 2006, Liptovský Ján Bacigál, T., Komorníková, M.: Fitting Archimedean copulas to bivariate geodetic data, - to appear in Proceedings of COMPSTAT 2006, August __ - September __, 2006, Rome, Italy |
Presentation:FSTA'06 (336kB).pdfFull paper:Magia'05 (274kB).pdfAplimat'06 (404kB).pdf Compstat'06 (136kB).pdf Calculations:Mathematica(265kB).nb.pdf(295kB).nb.zip |
|
| |
Modern multivariate approach to time-series modelling | |
Note:Written part of dissetation examination gather the meantime results of PhD research. It is mainly the modelling of cointegrated time-series (linear models) and multiregime processes with sharp transition function (nonlinear models). Besides, it contains propositions of the thesis project, and prospective contributions of the final thesis. |
Presentation:half_thesis (134kB).pdfFull paper:half_thesis (424kB).pdf |
|
| |
Testing for common deterministic trends | |
Abstract:GPS observations that are daily gathered to monitor recent kinematics of the Earth's crust yield three topocentric horizontal coordinate time series (north, east, vertical) per each carefully selected point (permanent station). Due to the long-term drift of the Eurasian tectonic plate two of the time series (those in horizontal plane) show visible linear trending with hight level of fit. Applied tests revealed a deterministic character of all the trends for both north and east direction. However, the point of this article is to test the time series for common deterministic trend slopes using multivariate analysis proposed by Vogelsang and Franses (2001). Getting grouped according to direction, most of the time series clearly follow the same common trend and similar results were obtained after transforming the north-east system into common trend direction. Results here support the idea that most of the monitored points move with the tectonic plate reflecting no significant regional movement.Published:Bacigál, T.: Testing for Common Deterministic Trends in Geodetic Data,- Proceedings of abstract of conference ISCAM 2005, Bratislava 15-16.April 2005 - Journal of Electrical Engineering, Vol. 56, No. 12/S, 2005, 115--118 |
Presentation:ISCAM'05 (123kB).pdfFull paper:ISCAM'05 (816kB).pdf |
|
| |
Time-series modelling in the light of cointegration | |
Abstract:Advancements and automation on the field of measuring instruments provide us with quantum of more and more precise data to be further processed in an appropriate way. In our paper we deal with such a set of data arranged in time - time series - taken from continuous GPS observations on permanent station Borowiec which takes part in EUREF network for monitoring Earth's crust kinematics. The outcome is a set of point's coordinates in local horizontal system (n,e,v) of which we took those two making horizontal plane, i.e. (n,v), and compare three methods of statistical processing. First, we model two univariate time series as if they are independent, another way is to accept the interrelationship and model it as one bivariate time series. The third one incorporates geometrical nature of both variables and makes use of a common trend presence. As a criterion of model's suitability we used mean square error and mean percentage error of predicted values. Whole one subsection dwells on testing for the presence of stochastic trend and subsequently for a cointegration, which is essential when investigating the series for common stochastic trend. This is represented by augmented Dickey-Fuller test and Johansen's test, respectively. Having affirmed cointegration, we transform the (n,e) system to obtain a new one, (y,x), oriented according to the common deterministic (linear) trend. This is processed on as usually and transformed back, finally. The usual procedure consists of trend and seasonality decomposition and applying the autoregressive models to still correlated residuals. Mean square and mean percentage errors computed for 5 predicted values per variable speak very clearly for the model supporting cointegration.Published:Bacigál, T., Komorníková, M.: Modelling point’s position time series in the light of cointegration,- Proceedings of INGEO 2004 (CD-ROM edition), INGEO 2004 Bratislava 11-13. 11. 2004 |
Presentation:Ingeo'04 (154kB).pdfFull text:Ingeo'04 (224kB).pdf |
|
| |
Modelling point's position time series with respect to common trend | |
Abstract:Points' position monitoring by means of Global Positioning System is in recent years an important point of interrest in Geodesy. Observations are highly automatized, and large amount of data in the form of time series is stored to subsequently be processed. The position is decomposed into three local horizontal coordinates (n, e, v) and further modeled by means of mathematical statistics. In this work three possible ways of modeling are discussed. We emphasize the procedure which respects a geometrical background (aspect) of the time series and takes advantage of common linear trend to transform the original data from north-east coordinate system into the one oriented according to trend direction. This is being compared with the other two methods which model original, north-east components by treating them as two independent univariate, and dependent bivariate time series, respectively.Published:Bacigál, T.: Modeling point’s position time series with respect to common trend,- Zborník príspevkov konferencie „PRASTAN 2004“, Kočovce 17-21. 5. 2004, 5--10 |
Presentation:Prastan'04 (492kB).pdfFull textPrastan'04 (409kB).pdf |
|
| |
Multivariate threshold autoregressive models | |
Abstract:In recent years, the situation in time series analysis has changed turning its concern from linear to nonlinear modeling. In this article we are trying to show how a special case of such a large family of models (as threshold autoregressive ones are) may be applied within processing of continual GPS observations. Two components (north and east) of point position in horizontal coordinate system are taken to obtain bivariate time series, which consequently are tested for nonlinearity and modeled using bivariate threshold autoregressive model. Whole procedure, of course, can be easily generalized to more than two-variate series.Published:Bacigál, T.: Multivariate threshold autoregressive models in geodesy,- Proceedings of abstract of conference ISCAM 2004, Bratislava 16-17.April 2004 - Journal of Electrical Engineering, Vol. 55, No. 12/S, 2004, 91--94 |
Presentation:ISCAM'04 (244kB).pdfFull paper:ISCAM'04 (392kB).pdfCalculation:Mathematica(195kB).nb.pdf(160kB).nb.zip |
|
| |
Least square spectral analysis | |
Summary:The thesis gives a detailed description of theoretical basis of least-squares spectral analysis (LSSA). At first, a common view into one-dimensional data series processing is given, as well as an existing procedures classification. Then, a necessary description of frequent analysis, used for time series to be analyzed in spectral domain,called Fourier spectral analysis is given better to understand it's relation to LSSA. There is a short review of basic ideas, as presented by it's author P.Vaníček, and consequently a minute description using the language of functional analysis. Two major applications are mentioned. First one deals with a problem of computing the spectrum of a complet time series, the second one is to remove some constituents before computing the spectrum of residuals, but in one run. Lastly, a derivation of probability density function (underlining the least-squares spectrum) and formulation of criteria for statistical significance of the least-squares spectral peaks is performed.Experimental section is oriented to test the powerful software implementation, named LSSA, on artificial time series, further to perform spectrum determination and systematic parameter estimation of observed time series. These originate from observing the position on GPS permanent stations (HFLK, BOR1) involved in CERGOP project. This thesis wants to highlight significant properties of LSSA, e.g. non-stationary and unequally spaced data series processing, fully populated covariance matrix integrating and possibility to compute any real frequency. Note:The diploma thesis was elaborated too theoreticaly, the topic is worth applying to some serious geodetic problem. I would appreciate if anyone eager to reprogramme the existing but non-stable fortran-based application dedicates his time to this promising theme. I can provide all the necesary resources for successful start. |
Full paper:DiplThesis (449kB).pdfLanguage:Slovak |
|
| |
Computerization of geodetic calculations by means of programing languages | |
Summary:Making use of programming language C++ and Delphi to solve some specific geodetic problems. Computation of parameters and points coordinates of comunication track given as simple circular arc. Computation of polar bar, forward intersection, resection, Hansen’s problem, reduction of some observables.Note:The Student scientific conference in April 2002 was the very end of my programmer's endeavour during the university study. It had begun within Programming, the first subject I failed to pass the exam in, by the way. Dead sure it wasn't my failure, so it sapped my confidence to one person and system of education he represented. Anyway, my zeal for programming forced me to spend the following summer holidays by creating algorithm in C for computing the simple circular arc coordinate solution. Then I met one charismatic person at the Department of Geodesy, Andrej Villim, who involved me into student scientific conferences and suddenly the education became a "serious fun". And we were having a lot of fun. After som period of time, the eagerness and free time resources passed away. That's why I admire any effort of sudents to do more than they are supposed to, and I'm looking forward to hearing from anyone who keeps his creativity dominating his consumerism.Software application:"zgu.zip" (412kB) Elementary geodetic problems (Win32)"obluk.zip" (51kB) Simple circular arc coordinate solution (DOS) |
Full paper:SVK 2002 (422kB).pdfSoftware:EGProblems (412kB).zipCircArc (51kB).zip Language:Slovak |
|
| |
Hardware and software for geoinformation systems | |
Note:Bachelor thesis from the 2001 is in many ways definitely not a hot issue today, actually it could even be acknowledged a historical value :) |
Full paper:BachThesis (344kB).pdfLanguage:Slovak |
|
| |
