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In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from a visible geometrical view. As an example, the roadmap of such inner transformation is presented based on a simple multiple linear regression model in this work. By applying the matrix algorithms like singular value decomposition (SVD) and Moore-Penrose generalized matrix inverse, the dependent variable vector lands into the right space of the independent variable matrix and is metamorphosed into regression coefficient estimator vector through the three-step of inner transformation. This work explores the geometrical relationship between the dependent variable vector and regression coefficient estimator vector as well as presents a new approach for vector rotating.

Long-term regional convergence hypothesis is examined for 32 Mexican states in a regional growth model with poverty traps using a new dataset on regional income inequality for the period 1940-2011. Although zero-growth poverty trap hypothesis is rejected for 28 out of 32 states, the evidence confirms alfa- convergence and beta-convergence for the period 1940-1980 and indicates the breakup of convergence in post-1980 period. The break in the convergence process is attributed to trade liberalization carried out under weak state capacity and clientelistic patronage environment without independent and effective regulators. The widening of regional inequality is characterized by an increase in growth in high-income U.S.-border states and no such increase in poorer states that cannot converge to the frontier under such conditions. When long-term convergence relationship is conditioned on unobserved long-run effects, the speed of convergence for pre-1980 period is around 2% per year and diminishes with the estimation horizon. Sensitivity analysis based on income-specific quantile regressions emphasizes substantial heterogeneity in the speed of convergence across states

Može se zaključiti da je knjiga namijenjena studentima ekonomije i srodnih disciplina s obzirom na način pisanja samog teksta, brojnih ekonomskih primjera. Dodatno, može predstavljati i podsjetnik onima koji na radnom mjestu moraju obrađivati podatke, te odraditi ekonometrijske analize. Nadalje, knjiga predstavlja uvod u ekonometriju, stoga je dovoljna za one koji se prvi puta susreću s tom tematikom, a da se ne prestraše brojnih formula i izvoda. Mnoštvo primjera olakšat će inicijalno shvaćanje materije, koje ce se lakše nadograditi knjigama koje su više tehnički pisane (s više izvoda, teorema i formula). Iako knjiga ne ide u dubinu većine gradiva, što nije ni nužno jer joj je sam naziv Uvod u ekonometriju, predstavlja dobar temelj za kretanje u to područje.

Kvantitativne financije danas predstavljaju neizostavan dio cjelokupnoga menadžmenta portfelja. Pritom je potrebno imati znanja iz područja financija, matematike, ekonometrije i statistike. Knjiga Financial Econometrics, Mathematics and Statistics predstavlja kombinaciju godina predavačkog iskustva, kao i onoga u istraživanjima troje autora.

Ova knjiga je namijenjena prvenstveno onima koji se primarno bave izučavanjem ekonometrije, vremenskih serija s teoretske strane ; dakle nastavnicima, te onima koji se intenzivno bave ekonometrijskim analizama u svojemu poslu, stoga moraju temeljno proći i teoriju kako bi što kvalitetnije provodili vlastita istraživanja. Dodatno, namijenjena je svim studentima viših godina studija koji žele kvalitetno savladati teoriju iz ekonometrije za pripremu za budući posao. Pritom je potrebno imati već određenu podlogu iz matričnog računa i teorije vjerojatnosti.

Knjiga Applied Time Series Analysis upravo kako joj sam naziv govori, predstavlja skup pojmova, definicija, modela i njihovih primjena u području modeliranja i prognoziranja vremenskih serija. Naime, u današnje doba prognoze koje su jako bliske sadašnjosti (jako bliska budućnost i prošlost) (engl. nowcasting) i prognoziranje općenito (engl. forecasting) veoma je važno u poslovnoj ekonomiji i makroekonomiji.

U posljednjih nekoliko godina uočava se ubrzano povećanje broja udžbenika iz ekonometrije, s obzirom na povećanje njene popularnosti, posebice u ekonomiji. Danas postoji mnogo knjiga koje se bave specifičnom temom ili dijelom ekonomije (vremenske serije, financijske vremenske serije, nelinearni modeli, itd.). Stoga nije lako privući pozornost novom materijom, osim ako se ona po određenim karakteristikama ne izdvaja u odnosu na masu. Knjiga An Introduction to Econometric Theory izdvaja se u odnosu na postojeću masu time što je namijenjena onima koji žele produbiti teorijska znanja iz ekonometrije. Autor sam na početku preporuča knjige iz područja primijenjene ekonometrije koje su komplementarne ovoj knjizi. Stoga se ova knjiga preporuča onima koji imaju određenu matematičku podlogu, posebice iz linearne algebre i teorije distribucija.

Knjiga GARCH Models. Structure, Statistical Inference and Financial Applications, Second edition preporuča se svima onima koji se bave financijskom ekonometrijom te žele produbiti postojeća znanja i proširiti ih novijima. Knjiga pripada skupini srednje do više razine težine, s obzirom na način na koji je pisana kroz teoreme, dokaze i slično. Prije čitanja ove knjige, preporuča se najprije proći određene udžbenike koji čitatelju daju određenu razinu znanja iz ekonometrije vremenskih serija. Na taj način će se lakše pratiti materija u ovoj knjizi. No, autori su se potrudili uključiti nove izvore literature kako bi čitatelje upoznali s najnovijim doprinosima u ovome području. Stoga ovo predstavlja dodatnu vrijednost knjige

Maģistra darbs “Dzimumu atalgojuma nevienlīdzības novērtēšana izmantojot Blinder-Oaxaca regresijas modeli” ietver sevī pētījumu par atalgojuma nevienlīdzības novērtēšanu starp dzimumiem ar mērķi precizēt esošo nepielāgoto rādītāju, kas atspoguļo doto problēmu, iekļaujot tā aprēķinā faktorus, kas ietekmē nodarbinātā atalgojuma līmeni. Pētījuma rezultāti sniedz priekštatu par dzimumu atalgojuma nevienlīdzības rādītāju, kur tiek iekļauti tie ietekmes faktori, kuri noved pie nodarbinātā noteiktā atalgojuma līmeņa sasniegšanas. Analizējot CSP Darbaspēka apsekojuma nodarbināto sniegtos datus, tika iegūts rādītājs, kurš atspoguļo nevienlīdzības līmeni, neatkarīgu no tādiem atalgojumu ietekmējošiem faktoriem kā nodarbinātā ieņemamais amats, slodze, izglītības līmenis un darba vietas darbības nozare., The Master thesis “Gender wage gap evaluation using Blinder-Oaxaca decomposition model” includes a study on assessing the gender wage inequalities, with an aim to clarify the existing unadjusted indicator, which does not include any wage impact factors. The results of the study provide a clear perspective on gender pay inequality, where concept “equal pay for equal job” is being performed. Analysis of the employee data from the Labour Force Survey of the Central Statistical Bureau resulted in an adjusted indicator reflecting the level of inequality, regardless of factors such as the position of the employee, the load, the level of education, the workplace sector.

Kvantitativne financije danas su jedno od područja za koje se sve ubrzanije razvijaju matematičke i statističke metode i modeli za primjenu u empiriji.Knjiga Nonparametric finance predstavlja doprinos u području kvantitativnih financija jer predstavlja nadopunu postojećoj literaturi koja se većinom temelji na parametrijskim metodama. Međutim, kako sam autor napominje na početku, potrebno je imati (posebice u određenim poglavljima) određeno matematičko predznanje. . Dodatno, radi se o kvantitativnoj knjizi, stoga se puno pažnje ne posvećuje financijskoj teoriji koju je potrebno znati za primjenu alata iz knjige. Stoga se knjiga preporuča onima koji imaju već određeno znanje iz financija i kvantitativnog područja, a žele ga dodatno potkrijepiti novim pojmovima ili već postojećim koji se nadograđuju u ovoj knjizi.

V delu diplomskega projekta smo s pomočjo ekonometričnih modelov skušali prikazati vpliv, ki ga je gospodarska kriza 2008 imela na produktivnost slovenskega gradbenega sektorja. V letih pred krizo je ta rasel po zavidljivih, morda celo previsokih stopnjah, s podobno intenzivnostjo pa je nato ta rast tudi upadla. V prvem delu smo postavili teoretično izhodišče o krizah in o gradbeništvu ter o njuni prepletenosti, v drugem delu pa bomo s pomočjo enostavnih regresijskih modelov skušali kvantificirati vpliv gospodarske krize na produktivnost dela v gradbenem sektorju. Produktivnost dela smo izbrali, ker je s strani OECD priporočana kot dobra mera za uspešnost gospodarstva ali sektorja, hkrati pa zaradi pomanjkanja četrtletnih podatkov o obsegu kapitala v sektorju nismo mogli analizirati modela multifaktorske produktivnosti. Pri analizi smo kot odvisno spremenljivko uporabili dodano vrednost gradbenega sektorja, kot neodvisno spremenljivko pa število opravljenih delovnih ur v sektorju. Vse podatke smo pridobili s spletne baze Eurostat, ki deluje pod okriljem Evropske komisije. Ocenili smo ekonometrični model za celotno obdobje (2000 – 2015) ter za dve podobdobji – pred in po nastopu krize. Ugotovili smo, da je njen vpliv nezanemarljiv, saj je padec produktivnosti dela velik – upadel je na približno 30% vrednosti pred krizo. The aim of the diploma project is to use econometric models to help quantify the impact of the 2008 economic crisis on the productivity of the Slovenian construction sector. The sector grew rapidly in the years leading up to the crisis, perhaps too rapidly, because the downfall was just as severe. In the first part we will present the theoretical aspects of the crisis and the construction sector as well as their connection. The second part aims to quantify the impact of the financial crisis on the construction sector, using simple regression models. We have decided to use labour productivity as recommended by OECD, because of the lack of quarterly capital data needed to design the more sophisticated multi-factor productivity model. Our dependent variable used was gross value added in the construction sector and our independent variable were hours worked in the sector. All of the data was taken from European Commision's Eurostat. We have specified the model for the entire period (2000 – 2015), as well as two extra models for the sub-periods before and after the crisis. We have come to the conclusion that the impact of the crisis was significant as the drop in labour productivity was very big – it fell to about 30% of the pre-crisis value.

Understanding the relationship between interest rates and term to maturity of securities is a prerequisite for developing financial theory and evaluating whether it holds up in the real world therefore, such an understanding lies at the heart of monetary and financial economics. Accurately fitting the term structure of interest rates is the backbone of a smoothly functioning financial market, which is why the testing of various models for estimating and predicting the term structure of interest rates is an important topic in finance that has received considerable attention for many decades. In this paper, we empirically contrast the performance of cubic splines and the Nelson-Siegel model by estimating the zero-coupon yields of Austrian government bonds. The main conclusion that can be drawn from the results of the calculations is that the Nelson-Siegel model outperforms cubic splines at the short end of the yield curve (up to 2 years), whereas for medium-term maturities (2 to 10 years) the fitting performance of both models is comparable. Razumevanje razmerja med obrestnimi merami in časom do dospelosti vrednostnih papirjev je osnovni pogoj za razvoj in ovrednotenje pravilnosti finančne teorije. Ta tematika je zato v osrčju monetarne in finančne ekonomije. Natančno prilagajanje terminske strukture obrestnih mer je hrbtenica tekoče delujočega finančnega trga. To je razlog, da je testiranje različnih modelov, ki ocenjujejo in napovedujejo terminsko strukturo obrestnih mer, na področju financ pomembna vsebina, ki je že nekaj desetletij deležna precejšnje pozornosti. V tem članku empirično primerjamo učinkovitost modela kubičnih zlepkov in Nelson-Sieglovega modela, tako da ocenimo donosnost brezkuponskih avstrijskih državnih vrednostnih papirjev. Ključni sklep, ki ga lahko izpostavimo na podlagi dobljenih rezultatov, je, da Nelson-Sieglov model bolje aproksimira brezkuponsko krivuljo donosa na kratkem koncu (do dveh let), na srednjem delu krivulje donosa (od dveh do desetih let) pa med rezultati obeh modelov ni bistvenih razlik.

This paper brings to light an economic problem that frequently appears in practice: For the same variable, more alternative forecasts are proposed, yet the decision-making process requires the use of a single prediction. Therefore, a forecast assessment is necessary to select the best prediction. The aim of this research is to propose some strategies for improving the unemployment rate forecast in Romania by conducting a comparative accuracy analysis of unemployment rate forecasts based on two quantitative methods: Kalman filter and vector-auto-regressive (VAR) models. The first method considers the evolution of unemployment components, while the VAR model takes into account the interdependencies between the unemployment rate and the inflation rate. According to the Granger causality test, the inflation rate in the first difference is a cause of the unemployment rate in the first difference, these data sets being stationary. For the unemployment rate forecasts for 2010-2012 in Romania, the VAR models (in all variants of VAR simulations) determined more accurate predictions than Kalman filter based on two state space models for all accuracy measures. According to mean absolute scaled error, the dynamic-stochastic simulations used in predicting unemployment based on the VAR model are the most accurate. Another strategy for improving the initial forecasts based on the Kalman filter used the adjusted unemployment data transformed by the application of the Hodrick-Prescott filter. However, the use of VAR models rather than different variants of the Kalman filter methods remains the best strategy in improving the quality of the unemployment rate forecast in Romania. The explanation of these results is related to the fact that the interaction of unemployment with inflation provides useful information for predictions of the evolution of unemployment related to its components (i.e., natural unemployment and cyclical component). V prispevku predstavljamo v praksi pogost ekonomski problem. Ko imamo za isto spremenljivko več napovedi, pri odločanju pa potrebujemo samo eno, je za izbiro najboljše treba te napovedi oceniti. Namen prispevka je predlagati nekaj strategij za izboljšanje napovedi stopnje brezposelnosti v Romuniji s primerjalno analizo točnosti na podlagi dveh kvantitativnih metod, Kalmanovega filtra in vektorskih avtoregresijskih modelov (VAR-modelov). Pri prvi metodi je upoštevan razvoj komponent brezposelnosti, pri VAR-modelih pa medsebojne odvisnosti med stopnjo brezposelnosti in inflacijsko stopnjo. Po Grangerjevem testu vzročnosti je inflacijska stopnja v prvi diferenci vzrok za stopnjo brezposelnosti v prvi diferenci pri stacionarnih podatkih. Za napovedi stopnje brezposelnosti v obdobju 2010-2012 v Romuniji dobimo z VAR-modeli (v vseh različicah VAR-simulacij) bolj točne napovedi kot s Kalmanovim filtrom na osnovi dveh modelov prostora stanj za vse mere točnosti. Upoštevajoč povprečno absolutno tehtano napako, so dinamične stohastične simulacije, uporabljene za napovedovanje brezposelnosti, ki temeljijo na VAR-modelu, najbolj točne. Pri drugi strategiji za izboljšanje začetnih napovedi, ki temelji na Kalmanovem filtru, so uporabljeni popravljeni podatki o brezposelnosti, transformirani s Hodrick-Prescottovim filtrom. Uporaba VAR modelov namesto različic Kalmanovega filtra je najboljša strategija za izboljšanje kakovosti napovedi stopnje brezposelnosti v Romuniji. Medsebojna povezanost med brezposelnostjo in inflacijo namreč ponuja uporabne informacije za napovedi, ki so zanesljivejše kot napovedi na osnovi razvoj brezposelnosti glede na gibanje njenih komponente (naravna brezposelnost in ciklična komponenta).

Konkurentnost željezničkog prijevoza u usporedbi s cestovnim se smanjuje, naročito na regionalnim željezničkim prugama. Kako bi se poboljšala ta situacija, EU je donijela razne direktive i pravila u svrhu povećanja učinkovitosti željezničkih poduzeća. U ovom radu predstavljamo organizacijski i ekonomski model koji se zasniva na europskoj politici vođenja lokalnog željezničkog sustava. Organizacijski model se temelji na analizi odluke o više kriterija. Za ekonomski smo model primijenili ekonometrijski pristup u procjeni funkcije troškova i marginalnih troškova na regionalnim prugama, koji predstavljaju osnovu troškova na željeznici. Primjenom takvog organizacijskog modela, poboljšat će se funkcioniranje željezničke mreže. Istraživanjem se ustanovilo da bi promjena postojećeg modela izračuna troškova korištenja infrastrukture donijela ekonomske koristi rukovodiocu željezničke infrastrukture i onima koji su zaduženi za promet. Primjenom predloženog modela također smo ustanovili da ima smisla povećati protok robe na nekorištenim željezničkim linijama jer su troškovi održavanja željezničke infrastrukture neelastični u odnosu na prevezene bruto tone., Competitiveness of rail transport compared to road transport has been reducing, especially on regional railway lines. To improve this situation, the EU adopted various directives and regulations to increase efficiency of railway undertakings. In this paper we present an organizational and economic model based on European policies for local railway system. The organizational model is based on multi-criteria decision analysis. For the economic model we used an econometric approach to estimate the cost function and marginal costs in regional lines, which constitute the basis for railway charges. By implementing such an organizational model, the functioning of the railway network will improve. The research found that a change in the existing model of calculating costs of infrastructure use would bring economic effects for the railway infrastructure manager and the providers of transport. Using the proposed model we also found that it is reasonable to increase the flow of goods on unused regional railway lines because the railway infrastructure maintenance costs are inelastic with regard to transported gross tons.

Magistrsko delo preučuje odnos med makroekonomskimi spremenljivkami in cenami stanovanjskih nepremičnin v štirih državah, Sloveniji, Avstriji, Nemčiji in v Veliki Britaniji. Raziskava temelji na metodi najmanjših kvadratov z namenom proučitve vpliva pojasnjevalnih spremenljivk, kot so bruto domači proizvod, realna višina dologoročnih obrestnih mer, stopnja brezposelnosti in drugih na odvisno spremenljivko, obravnavano v raziskavi, to je na indeks cene stanovanjskih nepremičnin. Podatki za analizo so pridobljeni iz sekundarnih virov, v obliki časovnih vrst. Podatke smo obdelali, da so bili primerni za analizo. Analizirali so izbrane makroekonomske kazalnike, za katere smo na podlagi preteklih raziskav in analiz predvidevali, da imajo vpliv na cene stanovanjskih nepremičnin. Tekom raziskave smo za vsako posamezno državo razvili linearni regresijski model in z metodo najmanjših kvadratov smo ocenili vpliv posameznega makroekonomskega kazalnika. Ob tem smo testirali vse zahtevane predpostavke metode najmanjših kvadratov, s čemer smo zagotovili verodostojne rezultate. This research examines the relationship between the changes of housing prices and the macroeconomic factors in 4 countries, in Slovenia, Austria, Germany and in Great Britain. This paper uses the Ordinary Least Square (OLS) method to capture the effect of independent variables, which are the Real Gross Domestic Product, the Real Interest Rate, the Unemployment Rate and others on the dependent variable, which is the Housing Price, measured with House Price Index. The data of the variables in this study are obtained through secondary sources. A time-series analysis is conducted to acquire the results. Some selected macroeconomic factors which have presumably influenced price movements are presented and analysed. During the research we developed 4 regression models for each observed country. The Ordinary Least Squares approach is used to assess the influence and power of macroeconomic factors that affect on housing price movements. During the research we tested all necessary assumptions to produce unbiased estimators using OLS.

Ovaj rad je detaljnija obrada članka autora Luce Pieronia i Mattea Ricciarellia pod nazivom: ”Modelling dynamic storage function in commodity markets: Theory and evidence” odnosno prevedeno na hrvatski : “Modeliranje funkcije dinamičkog skladištenja na tržištima roba: Teorija i dokazi”. U radu, slijedeći tzv. modernu teoriju skladištenja, modeliramo cijene robe u međuvremenskom okviru u kojem racionalni subjekt može prenositi robu kao zalihe iz trenutnog u buduće razdoblje zbog špekulativnih potreba i opreza. U prvom poglavlju opisujemo ekonomsku teoriju i motivaciju koja se nalazi iz svjetskog tržišta metala, konkretnije bakra. U drugom poglavlju uvodimo pojam Hamiltonijana te definiramo optimizacijski problem i ograničenja zajedno s postupkom optimizacije funkcije cilja. U trećem poglavlju navodimo potrebne alate za ekonometrijsku analizu dok u četvrtom poglavlju primjenjujemo navedene alate na podacima. U petom poglavlju komentiramo podatke i dobivene rezultate. U šestom poglavlju dajemo zaključak te komentiramo ponašanje ekonomskih agenata s obzirom na Tobinovo q. This paper is more detailed version of the article by authors Luca Pieroni and Matteo Ricciarelli: “Modelling dynamic storage function in commodity markets: Theory and evidence” . In this paper, by following so called modern theory of storage, we model commodity prices in an intertemporal framework, in which, a rational subject can carry commodity as stocks from present to the future period for speculative purposes and caution. In first chapter, we describe economic theory and motivation behind world metal market, particularly copper market. In second chapter, we introduce the Hamiltonian and define optimization problem with it's constraint together with optimization procedure. In third chapter, we mention necessary tools for econometric analysis while in fourth chapter, we apply those tools on our data. In fifth chapter, we comment on data and results. The conclusion is given the in sixth chapter, together with a comment on behaviour of economic agents with the respect to the Tobin's q.

V magistrskem delu se obravnava predvidevanje dnevne marginalne cene, ki se oblikuje na trgu za dan vnaprej. Delo se usmerjena v kratkoročno napovedovanje za dan vnaprej z znanimi podatki do prejšnjega dne. V nalogi je predstavljen elektroenergetski trg v Sloveniji, članici Evropske unije. Predstavljeno je delovanje sistema od proizvodnje do porabe s poudarkom na pomembnostih, ki vplivajo na trgovanje. Opisano je tudi delovanje borze, na katero se raziskava nanaša. Predvidevanje električne energije je izvedeno z linearnimi ekonometričnimi modeli, ki zajemajo borzne podatke časovnih vrst z dodanimi drugimi spremenljivkami. Rezultati predvidevanja kažejo, da lahko s takšnim modelom napovemo ceno električne energije za dan vnaprej, z dovolj majhnim intervalom napake. Proposed master thesis deals with the predicting of the daily marginal price determined by the market for the day ahead. The work focused on the short-term forecasting for the day ahead with known data until the previous day. The paper presents the electricity market in Slovenia, a member of the European Union. Presents the operation of the system from production to consumption with an emphasis on the importance of having an impact on trade. It also describes the operation of the power exchange on which the investigation relates. Prediction is carried out with linear econometric models, which include time series energy exchange data with the addition of other variables. Results projections show, that such model can predict the price of electricity for the day ahead, with enough small interval of error.

PurposeThe central task is to define the ties, existing between economic dimensions, which can be expressed in specific relations that require special attention during projecting to ensure they are not disrupted. The development of a computer‐based mathematical and economic model makes it possible to constantly monitor the condition of the entire economy of a given region, both from a global aspect, as well as by its individual sectors of activities.Design/methodology/approachEconomics employs a number of scientific disciplines and their methods, making this approach both multidisciplinary and interdisciplinary. Unlike the variables defined in the model–variables such as domestic product, the volume of fixed funds, the volume of new investment and employment, which change from year to year – the model parameters are considered constants for the entire period to which the model is applied. The parameter estimation indicates the extent to which the defined model is acceptable as a model of future regional economic and tourism growth.FindingsProviding the trends of past are unacceptable in the future period, the author proposes the use of structured policies, above all in the field of investments, to guide development in the desired direction. The author has addressed this particular issue through the example of a specific tourist region, and has tested and designed a development model not only for the regional economic system, but also for its tourism subsystem.Research limitations/implicationsAlthough they are suited to certain types of decisions, these methods have shown to be inadequate for other types, long‐term strategic decisions in particular, which require so‐called intuitive methods.Practical implicationsOptimal decision‐making in systems' operations is not possible without predictions pertaining to future economic development. The answers to numerous questions in estimating development factors are being provided by new methods, which seek to incorporate and assert an interdisciplinary approach, that is, a systematic approach in preparing decisions.Originality/valueThis methodology can be used in combination with “classical” methods of research, that will can help to recommend optimum development strategies for regional economic development.