Šiame darbe atliekami elektros energijos kainų analizė ir modeliavimas. Elektros kainų kitimui ir tokioms jų charakteringoms savybėms, kaip sezoniškumas, vidurkio reversija, darbo dienų, savaitgalio ir švenčių efektas, kintamumo klasterizacija, aprašyti taikomi SARIMA-TGARCH ir SARFIMA-TGARCH modeliai. Tyrimui naudojami kasvalandiniai Prancūzijos elektros energijos biržos kainų stebėjimai. Darbą sudaro dvi dalys – bendroji (teorinė) ir tiriamoji dalys. Pirmoje dalyje apžvelgiama literatūra bei aptariami teoriniai modelių aspektai: aprašomi ilgos atminties modeliai. Antroje dalyje pristatomi modelių empiriniai rezultatai: SARIMA-TGARCH ir SARFIMA-TGARCH modelių taikymas ir adekvatumo tikrinimas. / In this paper an econometric modelling and forecasting of electricity spot prices is presented. The aim of this work is to examine SARIMA-TGARCH and SARFIMA-TGARCH models for describing volatility of electricity spot prices and their characteristics such as season, mean reversion, volatility cauterization, and effects of workdays, weekends or holidays. The data of France electricity stock prices are used for analysis. This paper contains two parts – theoretical and empirical. In the first part the short review of literature is presented. Moreover, the theoretical aspects of long memory models are discussed. In the following part the empirical results are presented: application and adequacy examination of SARIMA-TGARCH and SARFIMA-TGARCH models.

The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J. K\"{o}rner in 1973. Although the notion of graph entropy has its roots in information theory, it was proved to be closely related to some classical and frequently studied graph theoretic concepts. For example, it provides an equivalent definition for a graph to be perfect and it can also be applied to obtain lower bounds in graph covering problems. In this thesis, we review and investigate three equivalent definitions of graph entropy and its basic properties. Minimum entropy colouring of a graph was proposed by N. Alon in 1996. We study minimum entropy colouring and its relation to graph entropy. We also discuss the relationship between the entropy and the fractional chromatic number of a graph which was already established in the literature. A graph $G$ is called \emph{symmetric with respect to a functional $F_G(P)$} defined on the set of all the probability distributions on its vertex set if the distribution $P^*$ maximizing $F_G(P)$ is uniform on $V(G)$. Using the combinatorial definition of the entropy of a graph in terms of its vertex packing polytope and the relationship between the graph entropy and fractional chromatic number, we prove that vertex transitive graphs are symmetric with respect to graph entropy. Furthermore, we show that a bipartite graph is symmetric with respect to graph entropy if and only if it has a perfect matching. As a generalization of this result, we characterize some classes of symmetric perfect graphs with respect to graph entropy. Finally, we prove that the line graph of every bridgeless cubic graph is symmetric with respect to graph entropy.

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model is formulated and it leads to a system of multi-time scale stochastic differential equations. The classical Picard-Lindel\"{o}f successive approximations scheme is expended to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this generates to a problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations. To illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are exhibited. Without loss in generality, the modeling and analysis of three time-scale fractional stochastic differential equations is followed by the development of the numerical algorithm for multi-time scale dynamic equations. The development of numerical algorithm is based on the idea if numerical integration in the context of the notion of multi-time scale integration. The multi-time scale approach is applied to explore the study of higher order stochastic differential equations (HOSDE) is presented. This study utilizes the variation of constant parameter technique to develop a method for finding closed form solution processes of classes of HOSDE. Then then probability distribution of the solution processes in the context of the second order equations is investigated.

We analyze by simulation the properties of two time domain and two frequency domain estimators for low order autoregressive fractionally integrated moving average Gaussian models, ARFIMA (p,d,q). The estimators considered are the exact maximum likelihood for demeaned data, EML, the associated modified profile likelihood, MPL, and the Whittle estimator with, WLT, and without tapered data, WL. Length of the series is 100. The estimators are compared in terms of pile-up effect, mean square error, bias, and empirical confidence level. The tapered version of the Whittle likelihood turns out to be a reliable estimator for ARMA and ARFIMA models. Its small losses in performance in case of ``well-behaved" models are compensated sufficiently in more ``difficult" models. The modified profile likelihood is an alternative to the WLT but is computationally more demanding. It is either equivalent to the EML or more favorable than the EML. For fractionally integrated models, particularly, it dominates clearly the EML. The WL has serious deficiencies for large ranges of parameters, and so cannot be recommended in general. The EML, on the other hand, should only be used with care for fractionally integrated models due to its potential large negative bias of the fractional integration parameter. In general, one should proceed with caution for ARMA(1,1) models with almost canceling roots, and, in particular, in case of the EML and the MPL for inference in the vicinity of a moving average root of +1. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

One of the main features of digital technology is that the digital media can be duplicated and reproduced easily. However, this allows unauthorized and illegal use of information, i.e. data piracy. To protect digital media against illegal attempts a signal, called watermark, is embedded into the multimedia data in a robust and invisible manner. A watermark is a short sequence of information, which contains owner&rsquo / s identity. It is used for evidence of ownership and copyright purposes. In this thesis, we use fractional Fourier transformation (FrFT) domain, which combines space and spatial frequency domains, for watermark embedding and implement well-known secure spread spectrum watermarking approach. However, the spread spectrum watermarking scheme is fragile against geometrical attacks such as rotation and scaling. To gain robustness against geometrical attacks, an invisible template is inserted into the watermarked image in Fourier transformation domain. The template contains no information in itself but it is used to detect the transformations undergone by the image. Once the template is detected, these transformations are inverted and the watermark signal is decoded. Watermark embedding is performed by considering the masking characteristics of the Human Visual System, to ensure the watermark invisibility. In addition, we implement watermarking algorithms, which use different transformation domains such as discrete cosine transformation domain, discrete Fourier transformation domain and discrete wavelet transformation domain for watermark embedding. The performance of these algorithms and the FrFT domain watermarking scheme is experimented against various attacks and distortions, and their robustness are compared.

This dissertation contains five essays in the field of time series econometrics. The main issue discussed is the lack of coherence between small sample and asymptotic inference. Frequently, in modern econometrics distributional results are strictly only valid for a hypothetical infinite sample. Studies show that the attained actual level of a test may be considerable different from the nominal significance level, and as a concequence, too many true null hypotheses will falsely be rejected. This leads, in the extension, to applied users that too often reject evidence in the data for theoretical predictions. In large, the thesis discusses how computer intensive methods may be used to adjust the test distribution, such that the actual significance level will coincide with the desired nominal level. The first two essays focus on how to improve testing for persistence in data, through a bootstrap procedure within a univariate framework. The remaining three essays are studies of multivariate time series models. The third essay considers the identification problem of the basic stationary vector autoregressive model, which is also the basic-line econometric specification for maximum likelihood cointegration analysis. In the fourth essay the multivariate framework is expanded to allow for components of different integrating order and in this setting the paper discusses how fractional cointegration affects the inference in maximum likelihood cointegration analysis. The fifth essay consider once again the bootstrap testing approach, now in a multivariate application, to correct inference on long-run relations in maximum likelihood cointegration analysis. / Diss. Stockholm : Handelshögsk.

Mt Kilimanjaro, Africa's highest mountain (5895m), is a large, young (<1.6Ma) stratovolcano at the southern end of the East African Rift, in northern Tanzania. Consisting of three distinct volcanic centres, Shira, Mawenzi and Kibo, Shira contains the highest proportion of mafic rocks. Shira samples are strongly silica under-saturated rocks, ranging from picro-basalt, to nephelinite and hawaiite (Mg numbers (Mg #) ranging from 77.2-35.5). Phenocrysts constitute up to 55% of some samples, and include aluminous augite (often containing abundant fluid and/or melt inclusions), olivine (Fo92-Fo49), plagioclase (An75-An42), nepheline (Ne77-Ne68), magnesiochromite and ulvöspinel. Groups identified on the basis of phenocryst assemblages and textures correlate with location. East Shira Hill samples contain olivine and clinopyroxene phenocrysts + microphenocrysts of plagioclase (Group 1), or plagioclase and clinopyroxene phenocrysts + microphenocrysts of olivine (Group 2). Samples with high Mg #'s contain abundant cumulate clinopyroxene and olivine (Fo92-Fo85). Group 3 samples (Shira Ridge) contain nepheline phenocrysts and Group 4 samples (Platzkegel) have distinct intergranular textures. Chondrite normalised REE patterns are steep, with light REE-enrichment up to 400x chondrite. Spider diagrams, normalised to OIB for primitive Shira samples have strong K depletions and Pb enrichments. The source of the Shira volcanic rocks is most likely an amphibole-bearing spinel lherzolite, in which amphibole remains residual. Similarities in spider diagram patterns and trace element ratios suggest a source similar to average OIB. The Shira volcanic centre is a polygenetic volcano, in which multiple small volume, low degree (4-10%) partial melts from a metasomatised subcontinental lithospheric mantle follow pre-existing structural weaknesses, before ponding in the lithosphere. Evolution of these small volume melts is dominated by shallow fractional crystallisation of clinopyroxene, olivine±spinel, with plagioclase also fractionating from Group 4 (Platzkegel) samples. A magma mixing origin is suggested for some samples and supported by complex zonation patterns in major and trace element chemistry of clinopyroxene phenocrysts as well as linear mixing arrays. The Shira volcanic centre has since ceased activity, and collapsed to form the present day Shira Ridge and caldera before being overlain by various Kibo and parasitic lavas to the east and northwest of the Shira region.

Thesis (Ph.D.)--University of Tulsa, 1985. / Bibliography: leaves 78-80.

Thesis (Ph.D.)--University of Tulsa, 1985. / Bibliography: leaves 78-80.

Στην παρούσα εργασία διερευνήθηκαν οι προσδιοριστικοί παράγοντες της επίδοσης των αποφοίτων της τριτοβάθμιας εκπαίδευσης (πανεπιστημιακής) στην Ελλάδα. Για τους σκοπούς της ανάλυσης χρησιμοποιήθηκαν στοιχεία διαστρωματικών χρονοσειρών σε επίπεδο πανεπιστημιακού τμήματος για την περίοδο 2001-2007 (Ελληνική Στατιστική Αρχή, ΕΛ.ΣΤΑΤ). Ως δείκτης επίδοσης χρησιμοποιήθηκε το ποσοστό των αποφοίτων με βαθμό πτυχίου “άριστα”, “λίαν καλώς” και “καλώς” και ως εκ τούτου το οικονομετρικό υπόδειγμα που εφαρμόστηκε είναι τύπου fractional logit. Βασιζόμενοι στην σχετική διεθνή βιβλιογραφία, ως επεξηγηματικές μεταβλητές χρησιμοποιήθηκαν πληροφορίες ανά πανεπιστημιακό τμήμα για την βάση εισαγωγής, το αντικείμενο σπουδών του τμήματος, την παλαιότητά του, το ποσοστό των φοιτητών που δηλώνουν ως τόπο κατοικίας την ίδια πόλη με αυτή της σχολής καθώς και την αναλογία φοιτητών ανά μέλη ΔΕΠ. Με βάση τα αποτελέσματα βρέθηκε ότι το αντικείμενο σπουδών και η παλαιότητα του πανεπιστημιακού τμήματος αποτελούν τους βασικούς προσδιοριστικούς παράγοντες της επίδοσης των αποφοίτων στα ελληνικά πανεπιστήμια. Να σημειωθεί ότι τα παραπάνω αποτελέσματα βρίσκονται σε συμφωνία με αυτά της σχετικής βιβλιογραφίας. / --