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BackgroundResearch suggests a general link between sexual boredom and sexual desire, but its understanding is currently very limited.AimTo identify distinct (latent) groups of women and men in long-term relationships based on their reported levels of sexual boredom and sexual desire.MethodsLatent profile analysis (LPA) was conducted in an online sample of 1223 Portuguese participants aged 18 and 66 years (mean ± SD, 32.75 ± 6.11), using indicators of sexual boredom and partner-related, attractive other–related, and solitary sexual desire to categorize participants. Multinomial logistic regression analysis was carried out to explore predictors and correlates of the latent profiles.OutcomesSexual boredom was assessed by the Sexual Boredom Scale, while sexual desire was measured with the Sexual Desire Inventory.ResultsAs compared with women, men reported higher levels of sexual boredom and sexual desire. LPA indicated 3 profiles in women and 2 profiles in men. Among women, P1 was characterized by above-average sexual boredom, below-average partner- and attractive other–related sexual desire, and very low solitary sexual desire; P2 by below-average sexual boredom, attractive other–related sexual desire, and solitary sexual desire and above-average partner-related sexual desire; and P3 by above-average sexual boredom, attractive other–related sexual desire, and solitary sexual desire and below-average partner-related sexual desire. In men, P1 was characterized by high sexual boredom, above-average partner-related sexual desire, and high attractive other–related and solitary sexual desire and P2 by below-average sexual boredom and above-average partner-related, attractive other–related, and solitary sexual desire. The latent profiles did not differ according to relationship duration. Overall, the sole consistent correlate of the latent categorization was sexual satisfaction.Clinical ImplicationsIn women, above-average levels of sexual boredom were linked to below-average levels of partner-related desire, which suggests likely benefits of helping the couple to minimize or cope better with their sexual routines. In men, participants in the 2 profiles did not differ in partner-related sexual desire, suggesting that clinical interventions dealing with male sexual boredom should investigate factors beyond the current relationship.Strengths and LimitationsThis study explored different facets of sexual desire and used LPA, rendering advantages over previous research. The male sample has lower statistical power than the female sample.ConclusionPatterns of sexual boredom and sexual desire among individuals in long-term monogamous relationships are distinct and consistently related to sexual satisfaction in women and men and to relationship satisfaction among only women, which have important clinical ramifications.

sj-pdf-13-hpq-10.1177_13591053231164542 for A meta-analytic exploration of associations between religious service attendance and sexual risk taking in adolescence and emerging adulthood by Goran Koletić, Luka Jurković, Azra Tafro, Goran Milas, Ivan Landripet and Aleksandar Štulhofer in Journal of Health Psychology

Supplemental material, sj-docx-14-hpq-10.1177_13591053231164542 for A meta-analytic exploration of associations between religious service attendance and sexual risk taking in adolescence and emerging adulthood by Goran Koletić, Luka Jurković, Azra Tafro, Goran Milas, Ivan Landripet and Aleksandar Štulhofer in Journal of Health Psychology

Adolescents and emerging adults are more likely to have unprotected sex and to have multiple partners compared to older adults, which puts them at a greater risk of contracting sexually transmitted infections (Panchaud, Singh, Feivelson, & Darroch, 2000). A growing body of research indicates that religiosity is a protective factor in decreasing sexual risk-taking behavior among adolescents (Haglund & Fehring, 2010). However, studies that assessed the relationship between religiosity and sexual risk taking have reported mixed findings. While some studies reported positive associations, others found negative associations or no links at all (Rostosky et al., 2004; Zimmer-Gembeck & Helfand, 2008; Boislard, van de Bongardt & Blais, 2016). Few efforts have been made to empirically review and synthesize these findings. The primary purpose of this study is to systematically review and synthesize the literature concerning the relationship between frequency of religious service attendance and sexual risk-taking behavior among adolescents and emerging adults.

Adolescents and emerging adults are more likely to have unprotected sex and to have multiple partners compared to older adults, which puts them at a greater risk of contracting sexually transmitted infections (Panchaud, Singh, Feivelson, & Darroch, 2000). A growing body of research indicates that religion may be a protective factor for sexual risk taking in adolescence and emerging adulthood (Haglund & Fehring, 2010). However, studies that assessed the relationship between religiosity and sexual risk taking have reported mixed findings (Rostosky et al., 2004; Zimmer-Gembeck & Helfand, 2008; Boislard, van de Bongardt & Blais, 2016). These inconsistencies and conflicting findings could reflect different psychosocial mechanisms that underlie the link between sexual risk-taking behaviors on the one hand and ritualistic aspects of religiosity (i.e., formal religiosity) and more intrinsic aspects—such as personal faith and importance attached to being a religious person (Nonnemaker, McNeely, & Blum, 2003; Regnerus, 2003) on the other hand. Religious service attendance may serve as a form of social integration that increases the opportunities for social support and reinforces internalization of religious group’s norms or peer pressure from religious friends, thus reducing the possibility of risky sexual behavior. In contrast, personal faith may reflect the of internalization of religious values and rules that may affect one’s attitudes and norms on sexuality and sexual behavior. Due to the sparsity of systematic assessment and synthesis in this research field, the potential differences, and their consequences for understanding young people’s sexual risk taking remain underexplored. Following our previous meta-analysis that assessed the relationship between religious service attendance and sexual risk taking in adolescents and emerging adults (https://osf.io/swbx3), the purpose of this study is to systematically review the literature on associations between personal faith and sexual risk-taking to enable comparisons between the role of religiosity and faith in young’s people sexual risk taking.

Utilizing the Bayesian statistical approach, this study aimed to test two competing claims: that religiosity and faith play a role vs. that they do not play a role in emerging adults’ sexual risk taking. The test included drawing on international evidence from the past two decades (Koletić et al., 2021), as well as on the data from two population studies of emerging Croatian adults carried out in 2010 and 2021. The second study aim was to establish the direction of a possible link between religiosity/faith and sexual risk taking. Finally, we explored whether the association between religiosity/faith and sexual risk taking is stronger in female or male emerging adults.

Each specific type of forest ecosystem has its own specific microclimate that depends on the macroclimate of the wider area, relief as well as the structural elements of the forest stand. Since the microclimate affects certain ecological and biological processes in the forest ecosystem, its study is a big part of research on forest biodiversity and its relationship to climate. Data on air and soil temperature, relative air humidity and soil moisture were collected over a longer period of time, with great frequency, at multiple forest stands near Vinkovci. This type of data poses a challenge with its size, multidimensionality with highly correlated variables, and different types of seasonality, but also provides a great opportunity for new insight. Given the complexity of the data, simple models generally do not perform well, and computationally complex state-of-the-art models are required. In this paper, the authors evaluate different time series models for the pedunculate oak forest microclimate data and attempt to provide statistical methodology for microclimate comparison between different plots.

Although there is some evidence that religiosity is related to lower levels of sexual risk taking among adolescents and emerging adults, no attempts have been made to systematically quantify the association. Using data from studies conducted since 2000 in samples of adolescents and emerging adults, this meta-analysis aimed to estimate the link between frequency of religious service attendance (extrinsic religiosity), religious faith (intrinsic religiosity), and four sexual risk-taking behaviors (age at sexual debut, number of sexual partners, condom use at most recent sexual intercourse, and consistent condom use). Five different search systems were used to conduct a systematic literature search in April 2020. Studies that contained quantitative data on religiosity (extrinsic or intrinsic) and at least one indicator of sexual risk taking were searched for. A total of 36 articles published in peer- reviewed journals were identified. Random-effects meta-analytic approach was used to assess sexual risk-taking associations with religious service attendance (k = 27, n = 37, 430, Mage = 18.4 years, 44% male), and religious faith (k = 22, n = 41, 758, Mage = 18.9 years, 37% male). The link between religious service attendance and sexual risk taking was significant only for age at sexual debut (r = .09, 95% CI = .05, .13) and the number of sexual partners (r = -.14, 95% CI = -.19, -.09). A weak association between religious faith on the one hand and age at sexual debut (r = .08, 95% CI = .03, .12) and the number of sexual partners on the other hand (r = -.15, 95% CI = -.21, -.09) was found. When religiosity is indicated by the frequency of religious service attendance or religious faith, the current meta- analysis found that religiosity is unlikely to protect young people against sexual risk taking. Considering the limited protective effect of religiosity, comprehensive sexuality education remains essential for the protection of reproductive and sexual health.

Light detection and ranging systems (LiDAR) that use laser light to measure distances are becoming increasingly popular in modeling and estimating forest attributes. By providing larger datasets than traditional field measurements they enable better model estimation, and modern computational methods allow for more complex models. However, there are currently no general guidelines for methods of testing and comparing the models. In this work, based on airborne LiDAR data and field measurements in lowland pedunculate oak forests of Pokupska basin, we provide a comprehensive overview of models and (cross-)validation methods and propose a possible best-practice standard in this setting.

Objective: Although there is some evidence that religiosity may be a protective factor against sexual risk taking in adolescence and emerging adulthood, no attempts have been made to systematically quantify the association. Using data from studies conducted in the 2000-2020 period, this meta-analysis aimed to estimate the link between frequency of religious service attendance (extrinsic religiosity), religious faith (intrinsic religiosity), and four sexual risk-taking behaviors in samples of adolescents and emerging adults. Design and Method: Five different search systems were used to conduct a systematic literature search in April 2020. Studies that contained quantitative data on religiosity (extrinsic or intrinsic) and at least one indicator of sexual risk taking (age at sexual debut, number of sexual partners, condom use at most recent sexual intercourse, and consistent condom use) were searched for. A total of 36 articles published in peer-reviewed journals were identified. Random-effects meta- analytic approach was used to assess sexual risk-taking associations with religious service attendance (k = 27, n = 37, 430, Mage = 18.4 years, 44% male), and religious faith (k = 22, n = 41, 758, Mage = 18.9 years, 37% male). Results: The link between religious service attendance and sexual risk taking was significant only for age at sexual debut (r = .09, 95% CI = .05, .13) and the number of sexual partners (r = -.14, 95% CI = -.19, -.09). A weak association between religious faith on the one hand and age at sexual debut (r = .08, 95% CI = .03, .12) and the number of sexual partners on the other hand (r = -.15, 95% CI = -.21, -.09) was found. Conclusions: When religiosity is indicated by the frequency of religious service attendance or religious faith, the current meta-analysis found that religiosity is unlikely to protect young people’s sexual and reproductive health.

U knjizi su sadržani zadaci s općinskih, županijskih i državnih natjecanja, zatim zadaci s Hrvatske matematičke olimpijade, Hrvatske juniorske matematičke olimpijade, Međunarodne matematičke olimpijade, Srednjoeuropske matematičke olimpijade i Juniorske balkanske matematičke olimpijade.

In addition to classical (time-consuming and labor-intensive) field measurements, remote sensing methods can be used to estimate various forest attributes at individual tree, plot or stand level. Remote sensing methods can reduce field work and improve the efficiency, but the accuracy of obtained results have to be carefully tested and evaluated. In this study, plot level volume of pedunculate oak forest was estimated using metrics extracted from digital surface model derived from aerial images and normalized using digital terrain model derived from airborne laser scanning. Traditional allometric equations for volume estimation are developed using linear regression on log- transformed data, which often causes bias in the estimation when errors are not additive. Several correction methods have been proposed to varying degrees of success, depending on the quantity of interest. Additionally, smaller sample sizes can cause poor goodness of fit, and greater variance in model error estimation. In this paper, the authors study bias in volume estimation, using multiple assessment and validation methods, to propose the optimal model for this type of data.

Background and Objectives: Despite increasing concerns that pornography decreases adolescents’ well-being, existing empirical support for this position is largely limited to cross-sectional studies. To explore possible links between adolescent pornography use and psychological well-being more systematically, this study focused on parallel dynamics in pornography use, self-esteem and symptoms of depression and anxiety. Methods: A sample of 775 female and 514 male Croatian high-school students (Mage at baseline = 15.9 years, SD = 0.52) from 14 larger secondary schools, who were surveyed six times at approximately 5- month intervals, was used for analyses. The longitudinal data were analyzed using latent growth curve and latent class growth modeling. Results: We observed no significant correspondence between growth in pornography use and changes in the two indicators of psychological well-being over time in either female or male participants. However, a significant negative association was found between female adolescents’ pornography use and psychological well-being at baseline. Controlling for group-specific trajectories of pornography use (i.e., latent classes) confirmed the robustness of findings in the both female and male samples. Conclusions: This study’s findings do not corroborate the notion that pornography use in middle to late adolescence contributes to adverse psychological well-being, but do not rule out such a link during an earlier developmental phase—particularly in female adolescents. The findings have ramifications for educational and adolescent health specialists, but also for concerned parents.

U knjizi su zadaci za općinsko/gradsko, županijsko i državno natjecanje, kao i zadaci s Hrvatske matematičke olimpijade, Hrvatske juniorske matematičke olimpijade, Međunarodne matematičke olimpijade, Srednjoeuropske matematičke olimpijade i Juniorske balkanske matematičke olimpijade.

Hill estimator for the tail index of regularly varying data is extensively studied in the statistics literature. Its consistency has been established in various settings, including that of dependent sequences of random variables. Building on their results, we show that the Hill estimator is consistent also when applied to stationary spatial lattice models under suitable conditions. We further show how these conditions can be checked in the case of spatial moving averages and moving maxima with regularly varying noise. Based on joint work with Bojan Basrak.

Let (Z_i, j) be i.i.d. random variables where the Z_i, j's have regularly varying tail probabilities. Then, under mild conditions on a real sequence (c_k, l), the stationary process (X_i, j) of moving averages of Z's (averaged by coefficients c_k, l) exists. By establishing a limit theory for point processes based on {;X_i, j}; we can explore approximations for probabilities of extremal events. This theory builds on results of Davis and Resnick for extremes of linear processes with heavy-tailed distributions.

U statistici često koristimo pretpostavku da su podaci međusobno nezavisni, no ona nije sasvim opravdana kada radimo s opažanjima koja su, zbog načina na koji su prikupljeni ili prirode problema kojeg opisuju, strukturirani u nekoliko grupa. Zbog toga uvodimo hijerarhijske modele, kod kojih je distribucija podataka za svaku grupu parametrizirana s θj, j = 1, 2, . . . , J, a odnos među parametrima modeliran je zajedničkom vjerojatnosnom distribucijom nad θ1, . . . , θJ. U okviru hijerarhijskih modela, posebno se ističe prednost bayesovskog pristupa, koji omogućava da pri donošenju zaključaka za jednu grupu iskoristimo i podatke o preostalim grupama. Bayesovsko hijerarhijsko modeliranje podrazumijeva da je i zajednička distribucija od θ1, . . . , θJ parametrizirana preko hiperparametara ϕ, za koje također promatramo apriornu i aposeriornu distribuciju i za koje donosimo statističke zaključke slijedeći bayesovske principe. U ovom smo radu iznijeli osnove bayesovske statistike, motivirali uvođenje hijerarhijskih modela te obradili bayesovsko hijerarhijsko modeliranje, s naglaskom na postavljanju modela i analizi dobivenih rezultata. Na primjerima su ilustrirane prednosti i glavne značajke bayesovskog hijerarhijskog pristupa modeliranju klasteriranih podataka, kao i metode računarske statistike korisne za prikaz rezultata. When doing statistical analysis, we often assume that data points are mutually independent. However, due to the way it was collected or the nature of the problem it came from, data is often structured into groups or clusters. In these situations, the assumption of independence comes into question. To tackle that, we introduce hierarchical models, where the probability distribution of data for each of the J groups is defined by the parameter θj and the relationship between these parameters is modeled by the joint distribution of θ1, . . . , θJ. Bayesian inference further broadens the use of hierarchical models because it enables us to make statistical conclusions about a certain group while incorporating information contained in the data belonging to other groups. In Bayesian hierarchical models, the joint distribution of θ1, . . . , θJ is defined by the hyperparameters ϕ, for which we also set a prior and calculate the posterior distribution using Bayesian inference. In this master’s thesis, we present the main theoretical results of Bayesian statistics, we discuss the motivation behind hierarchical modeling and give a detailed description of Bayesian hierarchical models, focusing on the procedure of setting up and analysing these models. We highlight the key advantages and principles of Bayesian hierarchical modeling using examples in which we also showcase computational methods for displaying results.

U ovome radu prezentiramo metodu sažimajućeg očitavanja koja nam omogućuje rekonstrukciju signala iz vrlo malog broja mjerenja, uz uvjet rijetkosti signala u nekoj bazi. Rekonstrukciju dobivamo preko problema minimizacije \(l_1\) norme, koja pod određenim uvjetima daje ista rješenja kao problem minimizacije \(l_0\) norme. U prvom poglavlju formuliran je problem sažimajućeg očitavanja i dana je usporedba s klasičnim pristupima sažimanju podataka. Uvedene su definicije i pojmovi koji se kasnije koriste. U drugom poglavlju detaljno je predstavljena teorija sažimajućeg očitavanja: pokazani su uvjeti pod kojima će postupak biti uspješan te su dane granice točnosti rekonstrukcije ovisno o parametrima mjerenja. U trećem poglavlju pokazali smo kako sažimajuće očitavanje radi u problemima rekonstrukcije slika, te smo uveli poboljšanja na sam postupak koja dovode do boljih rezultata rekonstrukcije. In this paper, we investigate compressive sensing, a technique that allows for the reconstruction of a signal from a limited number of measurements, provided that the signal exibits sparsity in some orthonormal basis. The signal is reconstructed by solving a \(l_1\) minimization problem is solved, which in the right conditions, yields a solution that is equivalent to a \(l_0\) minimization problem. In the first chapter, we formulate the compressive sensing problem and give compare it to the standard approach for signal compression. Key definitions and concepts are introduced. In the second chapter, we present a comprehensive theory of compressive sensing, demonstrating the conditions under which the method is guaranteed to be successful, and we providing the bounds on the reconstruction error based on the measurement process. In the third chapter, we demonstrate the application of compressive sensing to image reconstruction and modifications that significantly improve the reconstruction accuracy.

U ovom diplomskom radu predstavljamo jednu od brojnih primjena modela volatilnosti na izvedenice. U samom središtu je GARCH model koji je jedan od najznačajnijih i često korištenih modela volatilnosti za financijske vremenske nizove. Na početku, iznosimo već poznate rezultate i alate za vremenske nizove i njihovu primjenu u financijama. Dajemo uvid u modele volatilnosti kroz razumijevanje osnovnog koncepta volatilnosti, te motivaciju iza proučavanja takvih modela kao i primjenu istih za odredivanje cijena opcija. Takoder, ukratko uvodimo ARCH model koji je preteča GARCH modelu kojemu smo se detaljnije posvetili. Između ostalog, iskazujemo teorem o nužnom i dovoljnom uvjetu pri kojemu je GARCH(p,q) model slabo stacionaran, te u nastavku promatramo neke modifikacije samog modela i njegova proširenja. Slijedi okosnica ovog rada u kojoj promatramo model određivanja cijena opcija gdje uvjetna varijanca log-povrata financijske imovine prati GARCH(p,q) proces. Na kraju rad zaokružujemo praktičnim primjerom ilustriranim u programskom jeziku R gdje teorijske rezultate primjenjujemo na stvarnim podacima s tržišta za određivanja cijene europske call opcije i odgovarajuće delte. In this Master’s thesis, we present one of the many applications of the volatility model on derivatives. The focus is on the GARCH model as one of the most significant and frequently used volatility models for financial time series. In the beginning, we present the already known results and tools for time series and their application in finance. We provide insight into volatility models through understanding the basic concept of volatility, the motivation behind studying such models, as well as the application in option pricing. Also, we briefly introduce the ARCH model which is the forerunner of the GARCH model that we observe in more detail. Moreover, we present the theorem that gives the necessary and sufficient conditions under which the GARCH (p, q) model is weakly stationary. Furthermore, we observe some modifications of the model itself and its extensions. The following chapter is the backbone of this paper in which we present the option pricing model where the conditional variance of the log-return of financial assets follows the GARCH (p, q) process. Finally, we conclude the thesis with a practical example illustrated in the programming language R, where we apply the theoretical results to actual data for the european call option pricing and the corresponding delta.

Rizičnost vrijednosti, poznatija kao VaR, jedna je od mjera rizika u financijama koja se koristi širom svijeta, a predstavlja najveći mogući gubitak u nekom razdoblju. VaR možemo procijeniti na više načina. U ovom radu opisane su tri metode procjene VaR-a, a to su povijesna metoda, metoda varijance i kovarijance te Monte Carlo metoda. Povijesna metoda procjenjuje VaR pomoću povijesnih podataka te pretpostavlja da će se distribucija povrata u budućnosti ponašati isto kao u prošlosti. Metoda varijance i kovarijance parametarska je metoda koja procjenjuje VaR pomoću standardne devijacije i korelacije slučajnih varijabli za koje se pretpostavlja da su normalno distribuirane. Monte Carlo metoda, isto kao i povijesna metoda, spada u simulacijske metode. Ova metoda simulira veliki broj mogućih ishoda te računa VaR za svaki od tih scenarija. Uzimanjem aritmetičke sredine tako dobivenih VaR-ova dobijemo procjenu traženog VaR-a. Nakon procjene VaR-a bilo kojom od ovih metoda, potrebno je provesti testiranje unatrag. Testiranje unatrag je metoda u kojoj provjeravamo kvalitetu modela tako što procjenjujemo VaR u prošlosti te ga uspoređujemo sa stvarnim gubicima. Također, može se provesti testiranje otpornosti na stres kako bismo vidjeli ponašanje metoda za procjenu VaR-a u stresnim situacijama kao što su na primjer krizna vremena. U ovom radu, uz prethodno spomenutu teoriju, napravljena je primjena metoda za procjenu VaR-a te testiranja unatrag i testiranja otpornosti na stres na portfelj koji se sastoji od tri hrvatske dionice. Value at Risk (VaR) is one of the most popular risk measures in finance used around the world and it represents the largest possible loss over a period of time. VaR can be estimated with a few different methods. This paper describes three methods for estimating VaR, the historical method, the variance-covariance approach, and the Monte Carlo method. The historical method estimates VaR using historical data and assumes that the distributions of returns in the future will behave the same as in the past. The variance-covariance approach is a parametric method that estimates VaR using standard deviations and correlations of random variables that are assumed to be normally distributed. The Monte Carlo method is a simulation method same as the historical method. This method simulates a large number of hypothetical scenarios and calculates VaR for each of these scenarios. Our required VaR is the average of all of these values. After estimating VaR with one mentioned method, backtesting is needed. Backtesting is a procedure in which the quality of the model is checked by calculating VaR in past and comparing results with actual losses. Also, we can do stress testing to estimate VaR in stress scenarios like the financial crisis. This thesis also shows the application of methods, backtesting, and stress testing on a portfolio with three Croatian stocks.

Robusne statističke metode osmišljene su kako bi se suzbili neki od problema koji se pojavljuju kod klasične statističke analize, kao što su odstupanja od pretpostavki modela ili neuobičajene vrijednosti (outlieri). Posebno, kod procjene parametara modela linearne regresije, standardna metoda najmanjih kvadrata veoma je osjetljiva na opažanja koja znatno odstupaju od ostalih. Nakon predstavljanja općih modela jednostavne linearne regresije, višestruke linearne regresije i metode najmanjih kvadrata, uvedene su dvije mjere robusnosti - breakdown vrijednost i funkcija utjecaja. Zatim su prikazane dvije robusne metode, metoda najmanjeg medijana kvadrata odstupanja i metoda najmanjih odrezanih kvadrata. Za te dvije metode dokazano je da postižu maksimalnu breakdown vrijednost. U konačnici, ilustrirani su primjeri na stvarnim podacima radi usporedbe klasične metode najmanjih kvadrata sa robusnim metodama. Primjeri su radeni u programskom jeziku R. Robust statistical methods are designed to combat some of the problems that arise in classical statistical analysis, such as deviations from model assumptions and outliers. In particular, when estimating the parameters of a linear regression model, the standard least squares method is very sensitive to observations that deviate significantly from the others. After presenting the general forms of the simple linear regression model, multiple linear regression and the least squares method, two measures of robustness were introduced - the breakdown value and the influence function. Furthermore, two robust methods are presented, the least median squares method and the least trimmed squares method. These two methods have been shown to achieve a maximum breakdown value. Finally, examples with some real data and a comparison of the classical least squares method with robust methods are illustrated, using the programming language R.

Kreditni rizik je rizik neispunjavanja obaveza dužnika, a uz njega najčešće vežemo pojam defaulta, tj. neizvršenja novčanih obaveza. U ovom radu želimo pokazati kako procjenjujemo rizičnost dužnika, njegovo kretanje financijske imovine te vjerojatnost ulaska u default. Također, navodimo podjelu kreditnih modela na strukturalne i reducirane modele. Bavimo se strukturalnim modelima koji u fokus stavljaju vrijednost imovine poduzeća i pretpostavljaju da do defaulta dolazi kada vrijednost obaveza koje treba namiriti dosegne vrijednost imovine poduzeća. Predstavnik strukturalnih modela je Mertonov model koji se temelji na Black-Scholes- Mertonovom modelu pomoću kojeg smo odredili cijene financijske imovine. Kako Mertonov model ima jednostavnu strukturu, na kraju rada naveli smo i neka proširenja Mertonovog modela koja su nastala s ciljem da nadoknade nedostatke Mertonovog modela. Credit risk is a risk that a counterparty will not meet obligations, and it is most often associated with the term of default. In this thesis, we want to show how we assess the risk of the counterparty, his movement of financial assets and the probability of entering the default. We also state the division of credit models into structural and reduced models. We study structural models that focus on the value of the firm’s assets and assume that the default occurs when the value of the obligation to be settled reaches the value of the firm’s assets. A representative of the structural models is the Merton model based on the Black-Scholes- Merton model by which we determine the prices of financial assets. As Merton’s model has a simple structure, at the end of the thesis we have listed some extensions of Merton’s model that were created in order to compensate for the shortcomings of Merton’s model.

Faktorska analiza je statistička metoda čiji je cilj pronaći manji broj neopaženih varijabli (faktora) koje objašnjavaju što veći dio varijabilnosti početnoga skupa podataka. Početne varijable tada možemo prikazati kao linearne kombinacije faktora, iz čijih težina vidimo koliki je utjecaj određenog faktora na neku od varijabli. Razlikujemo eksploratornu i konfirmatornu faktorsku analizu, ovisno o tome jesu li nam faktori unaprijed poznati. U radu je objašnjena podjela varijance unutar faktorskog modela na komunalnost i jedinstvenu varijancu. Radi boljeg razumijevanja faktorske analize, dana je geometrijska interpretacija faktorskog modela i prikaz faktorskog prostora na primjeru dva zajednička faktora. Dalje, objašnjene su neke od metoda procjene potrebnog broja faktora i njihovih težina te mogućnost rotacije faktora. Na kraju rada ilustrirana je primjena eksploratorne faktorske analize u programskom jeziku R na skupu podataka koji analiziraju naslove novinskih članaka i osjećaje koje oni pobuđuju u čitatelju. Factor analysis is a statistical method that aims to find a smaller number of unobserved variables (factors) that explain as much of the variability of the initial data set as possible. The original variables can be modelled as linear combinations of the factors, whose weights represent the influence of a particular factor on the variable. Depending on our assumptions about factors, there are two types of factor analysis, exploratory and confirmatory. In this paper, the division of variance within the factor model into communality and unique variance is explained. A geometric interpretation of the factor model and an example of the factor space with two common factors are given. Methods for estimating number of factors and their loadings are explained, as well as rotations of the factors. In the end, an example of exploratory factor analysis is illustrated on a dataset that analyzes relations among news values and emotions using programming language R.

Monte Carlo simulacije su skup algoritama koji pomoću velikog broja izračuna i ponavljanja predviđaju ponašanje složenih slučajnih sustava. Pomoću njih procjenjujemo vrijednosti neke nepoznate varijable koristeći principe statističkog zaključivanja. Monte Carlo metode najčešće se koriste za rješavanje tri klase problema: integraciju, optimizaciju i generiranje slučajnih uzoraka iz vjerojatnosne distribucije. Problem kojim se bavimo u ovom radu je određivanje cijena izvedenica korištenjem Monte Carlo simulacija. Kako cijene izvedenica pod određenim pretpostavkama možemo računati kao očekivanje, procjenjujemo ih Monte Carlo integracijom. Koristimo Black-Scholes-Mertonov model financijskog tržišta u kojem cijene dionica modeliramo geometrijskim Brownovim gibanjem. Definiramo europsku call opciju, azijsku opciju i opciju izbora te pomoću Monte Carlo simulacija računamo cijene tih izvedenica. Kako bismo analizirali rizike na financijskim tržištima, definiramo Grke. Za računanje Grka Monte Carlo simulacijama koriste se posebne metode. Ukratko smo objasnili metodu izračuna po putu i pomoću nje simulirali izračun delta zaštite za portfelj koji se sastoji od europskih call opcija. Monte Carlo simulations are a set of algorithms which use a large number of calculations and repetitions to predict the behavior of complex random systems. We use them to estimate the values of an unknown variable using the principles of statistical inference. Monte Carlo methods are most commonly used to solve three classes of problems: integration, optimization and generation of random samples from a probability distribution. The problem we address in this thesis is the pricing of the derivatives using Monte Carlo simulations. As the prices of derivatives under certain assumptions can be calculated as an expectation, we estimate them by Monte Carlo integration. We use the Black-Scholes- Merton financial market model in which we model stock prices by geometric Brownian motion. We define the European call option, the Asian option and the Chooser option, and using Monte Carlo simulations we calculate the prices of these derivatives. To analyze the risks in the financial markets, we define the Greeks. Special methods are used to calculate the Greeks using Monte Carlo simulations. We briefly explain the pathwise method and use it to simulate the calculation of delta hedging for a portfolio consisting of European call options.

Model Gaussovih mješavina često se pojavljuje u raznim znanstvenim istraživanjima. Mješavina je populacija koja se sastoji od komponenata čije vjerojatnosne distribucije mogu, ali ne moraju nužno, pripadati istoj familiji distribucija. U ovom smo radu proučavali Gaussove mješavine čiji je broj komponenata konačan i unaprijed poznat. Za takve mješavine konstruirali smo model tako što smo procijenili distribucijske parametre svake komponente pa komponentama pridružili opažanja. Koristili smo metode procjene parametara iz teorije frekvencionističke i Bayesovske statistike koje su na kraju i objedinjene algoritmom maksimizacije očekivanja (EM algoritam). Svaki model mješavine potrebno je prilagoditi dostupnim informacijama o populaciji. Najjednostavniji slučaj koji modeliramo je kada su poznate gustoće komponenata pa im još preostaje pridružiti jedinke korištenjem Bayesovog naivnog klasifikatora. Ako su gustoće komponenata nepoznate, ali je poznata realizacija pridruživanja svakog opažanja, potrebno je samo procijeniti parametre gustoća. U tom smo slučaju procjenu proveli metodom maksimalne vjerodostojnosti kao i Bayesovom metodom. Za zadnji slučaj smo ostavili primjer populacije za koju unaprijed ne znamo niti parametre gustoća komponenata niti realizaciju pridruživanja jedinki. Taj je problem jednostavno riješen pomoću EM algoritma koji je u radu teorijski objašnjen, ali i realiziran na stvarnoj populaciji. Proces modeliranja Gaussovih mješavina ilustrirali smo na populaciji tri vrste pingvina i pritom za svaku jedinku odredili pridruživanje pomoću EM algoritma. Model smo izrazili kao linearnu kombinaciju višedimenzionalnih normalnih gustoća čije smo parametre procijenili. Gaussian mixture model occurs commonly in various scientific research. A mixture is a population that consists of components whose probability distributions could, but should not necessarily, belong to the same family of distributions. This thesis studies Gaussian mixtures whose number of components is finite and known in advance. For those mixtures, we constructed a model in a way that the distribution parameters were estimated and observations were assigned to the components. Parameter estimation methods that were used come both from frequentist and Bayesian statistics and are consolidated with the Expectation–Maximization algorithm (the EM algorithm). Each mixture model should be adjusted according to the available information on the population. The simplest case that is modelled is the one where densities of the components are known and only allocation of the observation remains. Allocation is conducted by using the naıve Bayes classifier. In the case where component densities are unknown and the allocation of the observations is known, only parameter estimation is required. Unknown parameters are estimated by using the method of maximum likelihood estimation along with the Bayesian method of estimation. The last studied case is the example of a population for which both the component parameters and the allocation is unknown. That problem is easily solved by using the EM algorithm which is in this thesis theoretically explained and implemented on the real–life population. The process of modelling Gaussian mixtures is illustrated on the population of three penguin species for which all the units are allocated to the components by using the EM algorithm. The model is given as a linear combination of multivariate normal distributions whose parameters were estimated.

U ovom su radu predstavljeni neki od modela koji procjenjuju vremenski promjenjive volatilnosti i korelacije multivarijatnih vremenskih serija. Za demonstraciju koristimo mjesečne log-povrate IBM dionice, S&P 500 indeksa Coca Cola dionice u razdoblju od siječnja 1963. godine do prosinca 2019. godine.Cilj analize multivarijatnih vremenskih serija je korištenjem stvarnih podataka više vremenskih serija procijeniti valjani model i proučiti međusobnu povezanost tih serija. Uvodimo osnovna svojstva ARCH i GARCH modela. GARCH modeli se primjenjuju u (financijskim) vremenskim serijama zato što pretpostavljaju da one imaju vremenski promjenjivu varijancu. Dodatni je razlog procjene korištenjem GARCH modela taj što financijske vremenske serije kao što su povrati pokazuju svojstvo grupiranja volatilnosti, što znači da vremenske serije imaju periode visoke i niske volatilnosti. Na procjenu EWMA modela i Modela dinamičke uvjetne korelacije (DCC) utječu jedan ili dva parametra te se zato često odbacuju dijagnostičkim provjerama. Jednostavni BEKK (Baba-Engle-Kraft-Kroner) model pruža općenit postupak za modeliranje multivarijatne volatilnosti, ali se susreće s poteškoćama u procjeni već za mali broj vremenskih serija. Također uvodimo postupak za modeliranje koji koristi Choleskyjevu dekompoziciju. Naposljetku, promatramo Go-GARCH model koji je prikladan i za velik broj vremenskih serija. In this paper, we present some models that explain how one estimates time-varying volatilities and correlations of multivariate time series. For demonstration, we consider monthly log-returns of IBM stock, S&P 500 index, and Coca Cola stock from January 1963 to December 2019. The objective of multivariate time series analysis is to study the past observations of a multiple time series to an adequate model that describes how the time series are interrelated. We give a brief description of the univariate ARCH and GARCH models. GARCH models are used in financial time series because they have time-varying variance. An additional reason for using GARCH models is a feature of time series called volatility clustering. Financial time series such as stock returns often exhibit volatility clustering, where time series show periods of high volatility and periods of low volatility. Models such as the Exponentially Weighted Moving Average (EWMA) model and Dynamic conditional correlation (DCC) model are extremely parsimonious because they estimate only one or two parameters. For that reason, they tend to be rejected by diagnostic checks. The simple Baba-Engle-Kraft-Krone (BEKK) model provides a general framework for estimating time-varying volatilities but encounters some difficulties in practice when the number of time series is large. We also give a procedure for multivariate volatility modeling using Cholesky decomposition. Finally, we employ the Go-GARCH model which is suitable for a large number of time series.

Analiza doživljenja je skup tehnika kojima se procjenjuje i opisuje vrijeme potrebno do pojave jednog ili više određenih događaja. U radu uvodimo osnovne pojmove analize doživljenja kao što su cenzuriranje i rezanje podataka, funkcija doživljenja, funkcija hazarda, kumulativna funkcija hazarda, očekivano trajanje života, itd. One su detaljno definirane u prva dva poglavlja. Prije njih navedene su osnovne definicije i pojmovi vjerojatnosti i statistike. U prvom poglavlju objašnjeni su tipovi podataka koji se obrađuju u analizi preživljavanja. Podaci mogu biti cenzurirani i odrezani. Postoji više vrsta svakog tipa, tako imamo lijevo i desno cenzurirane podatke, lijevo i desno odrezane podatke, intervalno cenzurirane podatke, te kombinacije. Veoma je bitno da prepoznamo s kakvim oblikom podataka radimo, jer se ovisno o njima mijenja i tehnika kojom procjenjujemo. Upoznajemo se s procjeniteljem maksimalne vjerodostojnosti za funkciju doživljenja, kojom procjenjujemo promatrane veličine. Detaljno obrađujemo teorijsku pozadinu parametarskog proporcionalnog modela rizika, stavljajući naglasak na Weibullov i eksponencijalni model doživljenja. Parametarski proporcionalni model rizika pretpostavlja da funkcija ovisi o prediktorskim varijablama na specifičan način. U konačnici, koristeći se principima definiranim u teorijskom dijelu, pobliže opisujemo pretpostavke PH modela te ističemo prednosti modela. Survival analysis is a set of methods for analysing time duration until one or more events happen. This paper introduces basic concepts of survival analysis such as censoring and truncation data, survival function, hazard function, the cumulative hazard function, the mean residual life function etc. They are considered in the second chapter. In the first chapter, we deal with the types of survival data. There are left and right censored data, left and right truncated data, interval censored data, and combination of them. It is important to know which type of data we have, because depending on that, we choose the techniques for estimation. We define maximum likelihood estimation of the survival function. The theoretical background for parametric proportional hazard model is developed. Weibull and exponential survival model are given as examples of the most commonly used specific models. Ultimately, using the principles defined in the theoretical part, we described the assumptions and prominent advantages of PH model.