Abstract This thesis describes the development of a new precipitation index-based conceptual water balance model with parameters easily regionalized through the functional relationship with catchment and climate attributes. It also presents a simple method for improving model dynamics for streamflow simulations in a non-stationary climate. The model was developed for streamflow modelling and prediction in high-latitude catchments, where model parameter regionalization is difficult due to limited availability of hydrological data for the region. The model couples a snow accumulation and melt formulation with a current precipitation index (CPI) formulation to simulate daily precipitation in runoff hydrograph pattern from catchments with seasonal snow cover. Using new runoff conversion factors CT and Lf, and a threshold flow factor ThQ, the simulated CPI hydrograph is converted into daily runoff and routed using the transformation function Maxbas. The model was developed in Microsoft Excel workbook and tested in 32 catchments in Finland, a region with considerable seasonal snow cover. The results showed that the model can adequately simulate and reproduce the dynamics of daily runoff from catchments where the underlying physical conditions are not known. In addition, incorporating temperature conditions influencing inter-annual variability in streamflow into the model structure improved its structural dynamics, thereby improving its performance in a non-stationary climate. Most model parameters showed strong relationships with observable catchment characteristics, climate characteristics, or both. The parameter functional relationships derived from the model parameter-catchment relationships produced equally good model results when applied to independent test catchments used as mock-ungauged catchments. Inclusion of snow-water equivalent records and use of multiple objective functions for snow-water equivalent and runoff simulations during model optimization helped reduce the effect of parameter equifinality, making it easier to determine optimal parameter values. The current precipitation index (CPIsnow) model is a parsimonious tool for predicting streamflow in data-limited high-latitude regions. / Tiivistelmä Tämä väitöskirja käsittelee yksinkertaisen sadantaan perustuvan konseptuaalisen vesitasemallin kehitystä ja soveltamista boreaalisille valuma-alueille sekä malliin liittyvää alueellista parametrisointia valuma-alueominaisuuksien ja ilmastoaineiston perusteella. Hydrologinen malli on luotu laskemaan ja ennustamaan valuntaa pohjoisille valuma-alueille, joilta on vähän hydrologista tietoa. Malli yhdistää lumen kertymisen ja sulannan tunnettuun sadantaindeksiin perustuvaan malliin (CPI) ja edelleen simuloi päivittäisen hydrografin valuma-alueille, joilla on selkeä lumipeitteinen ajanjakso. Malli laskee MaxBas funktion avulla CPI:llä muodostetun hydrografin päivittäiseksi valunnaksi valuntaan liittyvien malliparametrien CT ja Lf sekä virtaaman kynnysarvon ThQ avulla. Malli kehitettiin Excel-ympäristössä ja sitä testattiin 32 valuma-alueella Suomessa. Valuma-alueet edustivat maantieteellisesti kattavasti alueita, joilla esiintyy tyypillisesti kausittainen lumipeite. Saadut tulokset osoittivat, että kehitetty malli simuloi ja tuottaa päivittäisen valunnan riittävällä tarkkuudella valuma-alueille, vaikka hydrologista ja fysikaalista tietoa alueilta olisi niukasti. Useimmat malliparametrit olivat vahvasti riippuvaisia joko valuma-alue ominaisuuksista tai ilmastollisista parametreista tai molemmista. Parametrien funktionaalinen yhteys muodostettiin valuma-alueiden ominaisuuksien perusteella ja testattiin riippumattomalla valuma-aluejoukolla hyvin tuloksin. Malliparametrien samatavoitteellisuutta eli ekvifinaliteettiä voitiin vähentää huomioimalla mallissa lumen vesiarvomittaukset sekä hyödyntämällä useita parametrisia funktioita. Tällöin myös optimaalisten parametrien löytyminen nopeutui ja helpottui. Tämän väitöstyön pohjalta syntynyt uusi sadannan indeksiin pohjautuva laskentamalli (CPIsnow) mahdollistaa valunnan arvioinnin pieniltä valuma-alueilta, joilta on niukasti aineistoa saatavilla ja joissa lumen sulanta ja kertyminen ovat keskeisiä hydrologisia prosesseja.

Ce travail est centré sur la modélisation des dynamiques de volatilités et de corrélations entre rendements d'actifs financiers. Après une présentation de la littérature relative aux modèles Garch univariés et multivariés, l'auteur établit des résultats d'existence et d'unicité pour les solutions stationnaires des modèles de corrélations dynamiques de type DCC (Engle, 2002). Il étend ensuite cette classe de modèles en incluant les volatilités instantanées et des probabilités de changement de régime dans la dynamique des corrélations. Les nouveaux modèles sont évalués empiriquement sur un portefeuille d'indices MSCI. Des tests formels montrent que certaines de ces nouvelles spécifications améliorent le pouvoir prédictif de la matrice de covariance des rendements et s'avèreraient utiles en gestion de portefeuille. Enfin, se focalisant désormais sur le risque de volatilité, l'auteur montre que des stratégies de couvertures des principaux indices actions Européen à partir d'indices de volatilité implicite (VIX, VSTOXX) sont pertinentes et permettent à la fois de couvrir et réduire le risque action d'un portefeuille. / This work focuses on modeling the dynamics of volatilities and correlations between financial assets returns. After a literature review of univariate and multivariate GARCH-type models, the author establishes results for the existence and uniqueness of stationary solutions of dynamic correlations models (DCC model, Engle 2002). He then extends this class of models including instantaneous volatility and probability of regime changes in the dynamics of correlations. The new models are empirically evaluated on a MSCI portfolio. Formal tests have shown that some of these new specifications improve predictive power of the returns covariance matrix that would be useful in portfolio management. Finally, focusing now on the volatility risk, the author shows that hedging strategies of main European equity indices based on implied volatility indices (VIX, VSTOXX) are relevant and allow to both hedge and reduce the equity risk of a portfolio.

Abstract In this thesis, we consider autonomous environmental modelling, where robotic sensing platforms are utilized in environmental surveying. In order to allow a wide range of different environments, our models must be flexible to the data with some a prior assumptions. Respectively, in order to guide action planning, we need to have a unified sensing quality metric that depends on the prediction quality of our models. Finally, in order to be able to adapt to the observed information, at each iteration of the action planning algorithm, we must be able to provide solutions that aim at minimum travelling time needed to reach a certain level of sensing quality. These are the main topics in this thesis. At the center of our approaches are stationary and non-stationary Gaussian processes based on the assumption that the observed phenomenon is due to the diffusion of white noise, where diffusion kernel anisotropy and scale may vary between locations. For these models, we propose adaptation of diffusion kernels based on a structure tensor approach. Proposed methods are demonstrated with experiments that show, assuming sensor noise is not dominating, our iterative approach is able to return diffusion kernel values close to correct ones. In order to quantify how precise our models are, we propose a mutual information based sensing quality criterion, and prove that the optimal design using our sensing quality provides the best prediction quality for the model. To incorporate localization uncertainty in modelling, we also propose an approach where a posterior model is marginalized over sensing path distribution. The benefit is that this approach implicitly favors actions that result in previously visited or otherwise well-defined areas, meanwhile, maximizing the information gain. Experiments support our claims that our proposed approaches are best when considering predictive distribution quality. In action planning, our approach is to use graph-based approximation algorithms to obtain a certain level of model quality in an efficient way. In order account for spatial dependency and active localization, we propose adaptation methods that map sensing quality to vertex prices in a graph. Experiments demonstrate the benefit of our adaptation methods compared to the action planning algorithms that do not consider these specific features. / Tiivistelmä Tässä väitöskirjassa tarkastellaan autonomista ympäristön mallinnusta, missä ympäristön kartoitukseen hyödynnetään robottimittausalustoja. Erilaisia ympäristöjä varten, käytettävien mallien tulee olla joustavia datalle tietyillä a priori oletuksilla. Mittausalustojen ohjaus vaatii vastaavasti yhtenäisen, mallien ennustuslaadusta riippuvan, kartoituksen laatumetriikan. Mukautuakseen uuteen informaatioon, ohjausalgoritmin tulee lisäksi pyrkiä joka iteraatiolla minimoimaan tietyn kartoituksen laadun saavuttava kulkuaika. Nämä ovat tämän väitöskirjan pääaiheet. Tämän väitöskirjan keskiössä ovat sellaiset stationaariset ja ei-stationaariset Gaussin prosessit, jotka perustuvat oletukseen että havaittu ilmiö johtuu valkoisen kohinan diffuusiosta. Diffuusiokernelin anisotrooppisuudelle ja skaalalle sallitaan paikkariippuvaisuus. Tässä väitöskirjassa esitetään näiden mallien mukauttamiseen rakennetensoripohjaisia menetelmiä. Suoritetut kokeet osoittavat, että esitetyt iteratiiviset mukauttamismenetelmät tuottavat lähes oikeita diffuusiokernelien arvoja, olettaen, että sensorikohina ei dominoi mittauksia. Mallien ennustustarkkuuden määrittämiseen esitetään keskinäisinformaatioon perustuva kartoituksen laatumetriikka. Väitöskirjassa todistetaan, että optimaalinen ennustuslaatu saavutetaan käyttämällä esitettyä laatumetriikkaa. Väitöskirjassa esitetään lisäksi laatumetriikka, jossa posteriori malli on marginalisoitu kartoituspolkujen jakauman yli. Tämän avulla voidaan huomioida paikannusepävarmuuden vaikutukset mallinnuksessa. Tällöin etuna on se, että kyseinen laatumetriikka suosii implisiittisesti sellaisia mittausalustojen ohjauksia, jotka johtavat aeimmin kartoitetuille tai helposti ennustettaville alueille samalla maksimoiden informaatiohyödyn. Suoritetut kokeet tukevat väittämiä, että väitöskirjassa esitetyt menetelmät tuottavat parhaan ennustusjakauman laadun. Mittausalustojen ohjaus vaatii vastaavasti yhtenäisen, mallien ennustuslaadusta riippuvan, kartoituksen laatumetriikan. Väitöskirjassa esitetään mukautusmenetelmiä kartoituksen laadun kuvaukseksi graafin solmujen kustannuksiksi. Tämän avulla sallitaan sekä spatiaalinen riippuvuus että aktiivinen paikannus. Mittausalustojen ohjaus vaatii vastaavasti yhtenäisen, mallien ennustuslaadusta riippuvan, kartoituksen laatumetriikan.

Magister Scientiae - MSc / In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as ‘mean-unbiased’ and ‘medianunbiased’ estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1). However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to  compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the ‘medianunbiased’ estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed; the ‘most-probably-unbiased’ estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed; (2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model; (3) the exact variance and MSE of LS estimator is determined; (4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort; (5) an exact method of evaluating the density of the three estimators is described; (6) their exact bias, mean, variance and MSE are determined and analysed; and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed. The discussion and results show that the estimators are still biased in the usual sense: ‘in expectation’. However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation. / South Africa

This thesis deals with analysis and processing of the Sleep Electroencephalogram (EEG) signals. The scope of this thesis can be split into several areas. The first area is application of the Independent Component Analysis (ICA) method for EEG signal analysis. A model of EEG signal formation is proposed and conditions under which this model is valid are examined. It is shown that ICA can be used to remove non-deterministic artifacts contained in the EEG signals. The second area of interest is analysis of stationarity of the Sleep EEG signal. Methods to identify stationary signal segments and to analyze statistical properties of these stationary segments are presented. The third area of interest focuses on spectral analysis of the Sleep EEG signals. Analyses are performed that shows the processes that form particular parts of EEG signals spectrum. Also, random signals that are an integral part of the EEG signals analysis are performed. The last area of interest focuses on elimination of the transition processes that are caused by the filtering of the short EEG signal segments.

Die Risikohomeostasistheorie (RHT) ist ein formales Konzept zur Erklärung menschlichen Verhaltens im Straßenverkehr bei verändertem Unfallrisiko. Vor dem Hintergrund des gegenwärtigen Standes der Ökonometrie weisen die Untersuchungen zur RHT mittels langer Zeitreihen einige Schwächen auf. Im folgenden wird versucht, diese Schwächen einerseits mit dem Stationaritätskonzept der Ökonometrie und andererseits mit einer auf Dummyvariablen basierenden Methode zu beheben. Gleichzeitig wird die Theorie einem neuerlichen Test auf ihre Gültigkeit hinsichtlich der Unfallsituation im Straßenverkehr in Deutschland unterzogen. Die Arbeit nimmt Bezug erstens auf die Wirksamkeit von Regulierungsmaßnahmen (hier: Verschärfung der Gurtanlegepflicht) und zweitens auf die Wirkungen der deutschen Wiedervereinigung. Beiden Ereignissen wird nach der RHT keine Wirkung zugesprochen. Die Ergebnisse der Analysen unterstützen die Thesen der RHT nur schwach. Sie belegen, daß konsequente und mit Strafandrohung belegte Regulierungsmaßnahmen entgegen dem Postulat der Risikohomeostasisthese eine stark positive Wirkung auf die Unfallsituation besitzen. Außerdem werden die komplexen Entscheidungsprozesse von Verkehrsteilnehmern im Kontext mehrerer theoretischer Konzepte untersucht. Es zeigt sich, das Theorien zur Beschreibung individuellen Verhaltens unter Unsicherheit sehr gut geeignet sind, tatsächliches Verhalten von Verkehrsteilnehmern zu erklären. / Risk homeostasis theory (RHT) is a behavioural theory of risk taking in road traffic. So far, most of the published papers concerning RHT and long time series are based on econometric methods which are not very well suited for this purpose. We propose here to address the issue using instead the econometric concept of stationarity and a concept based on dummy variables. We then test the RHT with German traffic accident data and specifically analyze compulsory traffic safety measures (the penalty for not using seat belts) as well as the effects of German reunification. Both are ineffective according to RHT. Our results, found by using several risk measures, show only weak evidence for RHT. Contrary to RHT, we can show that compulsory safety measures combined with penalties had a strict positive effect on the road traffic accident risk. We also develop a solution which focuses on the complex decision-making process of an individual in road traffic. This is done within the context of several theories explaining individuals decision-making under uncertainty. There we can show that these theoretical concepts are very well suited to explain actual behavior of road users.

Collisionless shocks are widespread phenomena in the universe, and understanding the mechanisms behind their energy dissipation, with a rare number of collisions between particles, remains a significant unresolved question. The Earth’s bow shock provides an excellent opportunity to study this phenomena in situ. For high Mach number shocks, the shock cannot be sustained without partial reflection of the incoming ions. At higher Mach numbers, the shock surface starts to exhibit non-stationary behaviours, meaning that the shock surface starts evolving. One such behaviour is known as shock reformation, where a new shock forms upstream of an existing one. This study aims to investigate shock reformation using data obtained from NASA’s MMS mission, which offers precise measurements with high spatial and temporal resolutions through its constellation of four spacecraft. Using the MMS shocks database (Lalti et al., 2022), the gradient of the magnetic field magnitude is computed to infer non-stationary behaviour and identify potential instances of shock reformation and other shock behaviours. Through the analysis of the MMS measurements, some insight into the non-stationary characteristics of shocks is obtained using the gradient of the magnetic field. However, further analysis is needed in order to refine the method of identifying non-stationary behaviour of shocks, for future applications. / Kollisionsfria chocker är ett vanligt fenomen som förekommer i universum, och att förstå hur energidissipation inträffar i chocker med ett fåtal kollisioner mellan partikar är ett olöst problem. Jordens bogchock utger en bra möjlighet att studera detta på plats med mätningar från rymdfarkoster. Detta projekt försöker studera delar av jordens bogchock och undersöka dess dynamic. För chocker med högt machtal, måste en del av jonerna från solvinden reflekteras för att chocken ska skunna upprätthållas. Vid högre machtal kan chockytan visa icke-stationära beteenden, vilket innebär att den börjar förändras. Ett exempel på sådant beteende är chockreformation, där en ny chock formas framför en befintlig chock. Denna studie har som mål att undersöka chockreformation med hjälp av data som erhållits från NASA:s MMS-uppdrag, vilket erbjuder precisa mätningar med hög rumslig och tidsmässig upplösning genom sin konstellation av fyra rymdfarkoster. Genom användning av MMS-shockdatabasen (Lalti et al., 2022) beräknades gradienten av magnetfältets magnitud för att härleda icke-stationärt beteende och identifierade potentiella fall av chockreformation och andra beteenden. Genom analys av MMS-mätningarna erhölls viss insikt i de icke-stationära egenskaperna hos chocker med hjälp av gradienten av magnetfältet, men ytterligare analys krävs för att förbättra metoden för framtida tillämpningar.

<p>In this dissertation stochastic processes are regarded in the framework of Colombeau-type algebras of generalized functions. Such processes are called Colombeau stochastic processes.The notion of point values of Colombeau stochastic processes in compactly supported generalized points is established. The Colombeau algebra of compactly supported generalized constants is endowed with the topology generated by sharp open balls. The measurability of the corresponding random variables with values in the Colombeau algebra of compactly supported generalized constants is shown.<br />The generalized correlation function and the generalized characteristic function of Colombeau stochastic processes are introduced and their properties are investigated. It is shown that the characteristic function of classical stochastic processes can be embedded into the space of generalized characteristic functions. Examples of generalized characteristic function related to gaussian Colombeau stochastic<br />processes are given. The structural representation of the generalized correlation function which is supported on the diagonal is given. Colombeau stochastic processes with independent values are introduced. Strictly stationary and weakly stationary Colombeau stochastic processes are studied. Colombeau stochastic processes with stationary increments are characterized via their stationarity of the gradient of the process.Gaussian stationary solutions are analyzed for linear stochastic partial differential equations with generalized constant coefficients in the framework of Colombeau stochastic processes.</p> / <p>U disertaciji se stohastički procesi posmatraju u okviru Kolomboove algebre uop&scaron;tenih funkcija. Takve procese nazivamo Kolomboovi stohastički procesi. Pojam vrednosti Kolomboovog stohastičkog procesa u tačkama sa kompaktnim nosačem je uveden. Dokazana je merljivost odgovarajuće slučajne promenljive sa vrednostima u Kolomboovoj algebri uop&scaron;tenih konstanti sa kompaktnim nosačem,&nbsp; snabdevenom topologijom generisanom o&scaron;trim otvorenim loptama. Uop&scaron;tena korelacijska funkcija i uop&scaron;tena karakteristična funkcija Kolomboovog stohastičkog procesa su definisane i njihove osobine su izučavane. Pokazano je da&nbsp; se karakteristična funkcija klasičnog stohastičkog procesa može potopiti u prostor uop&scaron;tenih karakterističnih funkcija. Dati su primeri uop&scaron;tenih karakterističnih funkcija&nbsp; gausovskih Kolomboovih stohastičkih procesa. Data je strukturna reprezentacija uop&scaron;tene korelacijske funkcije sa nosačem na dijagonali. Kolomboovi stohastički procesi sa nezavisnim vrednostima su predstavljeni. Izučavani su strogo stacionarni i&nbsp; slabo stacionarni Kolomboovi stohastički procesi. Kolomboovi stohastički procesi sa stacionarnim prira&scaron;tajima su okarakterisani preko stacionarnosti gradijenta procesa. Gausovska stacionarna re&scaron;enja za linearnu stohastičku parcijalnu diferencijalnu jednačinu sa uop&scaron;tenim konstantnim koeficijentima su analizirana u okvirima Kolomboovih stohastičkih procesa.</p>

Cette thèse traite la contribution des méthodes d'ondelettes sur la modélisation des séries temporelles économiques et financières et se compose de deux parties: une partie univariée et une partie multivariée. Dans la première partie (chapitres 2 et 3), nous adoptons le cas univarié. Premièrement, nous examinons la classe des processus longue mémoire non-stationnaires. Une étude de simulation a été effectuée afin de comparer la performance de certaines méthodes d'estimation semi-paramétrique du paramètre d'intégration fractionnaire. Nous examinons aussi la mémoire longue dans la volatilité en utilisant des modèles FIGARCH pour les données de l'énergie. Les résultats montrent que la méthode d'estimation Exact Local Whittle de Shimotsu et Phillips [2005] est la meilleure méthode de détection de longue mémoire et la volatilité du pétrole exhibe une forte évidence de phénomène de mémoire longue. Ensuite, nous analysons le risque de marché des séries de rendements univariées de marchés boursier, qui est mesurée par le risque systématique (bêta) à différents horizons temporels. Les résultats montrent que le Bêta n'est pas stable, en raison de multi-trading stratégies des investisseurs. Les résultats basés sur l'analyse montrent que le risque mesuré par la VaR est plus concentrée aux plus hautes fréquences. La deuxième partie (chapitres 4 et 5) traite l'estimation de la variance et la corrélation conditionnelle des séries temporelles multivariées. Nous considérons deux classes de séries temporelles: les séries temporelles stationnaires (rendements) et les séries temporelles non-stationnaires (séries en niveaux). / This thesis deals with the contribution of wavelet methods on modeling economic and &#64257;nancial time series and consists of two parts: the univariate time series and multivariate time series. In the &#64257;rst part (chapters 2 and 3), we adopt univariate case. First, we examine the class of non-stationary long memory processes. A simulation study is carried out in order to compare the performance of some semi-parametric estimation methods for fractional differencing parameter. We also examine the long memory in volatility using FIGARCH models to model energy data. Results show that the Exact local Whittle estimation method of Shimotsu and Phillips [2005] is the better one and the oil volatility exhibit strong evidence of long memory. Next, we analyze the market risk of univariate stock market returns which is measured by systematic risk (beta) at different time horizons. Results show that beta is not stable, due to multi-trading strategies of investors. Results based on VaR analysis show that risk is more concentrated at higher frequency. The second part (chapters 4 and 5) deals with estimation of the conditional variance and correlation of multivariate time series. We consider two classes of time series: the stationary time series (returns) and the non-stationary time series (levels). We develop a novel approach, which combines wavelet multi-resolution analysis and multivariate GARCH models, i.e. the wavelet-based multivariate GARCH approach. However, to evaluate the volatility forecasts we compare the performance of several multivariate models using some criteria, such as loss functions, VaR estimation and hedging strategies.

Abstract of thesis submitted in partial fulfilment of the requirements for the Degree of Master of Commerce and Management Dynamics of macroeconomic variables in Fiji : a cointegrated VAR analysis By Shiu Raj Singh The objective of this study is to examine how macroeconomic variables of Fiji inter-relate with aggregate demand and co-determine one another using a vector autoregression (VAR) approach. This study did not use a prior theoretical framework but instead used economic justification for selection of variables. It was found that fiscal policy, which is generally used as a stabilisation tool, did not have a positive effect on real Gross Domestic Product (GDP) growth in the short term. Effects on GDP growth were positive over the long term but not statistically significant. Furthermore, expansionary fiscal policy caused inflationary pressures. Fiji has a fixed exchange rate regime, therefore, it was expected that the focus of monetary policy would be the maintenance of foreign reserves. It was, however, found that monetary expansion in the short term resulted in positive effects on real GDP growth and resulted in inflation. The long term effects of monetary policy on real GDP growth were negative, which are explained by the fixed exchange rate regime, endogenous determination of money supply by the central bank, an unsophisticated financial market and, perhaps, an incomplete transmission of the policy. Both merchandise trade and visitor arrivals growth were found to positively contribute to short term and long term economic growth. Political instability was found not to have significant direct effects on real GDP growth but caused a significant decline in visitor arrivals which then negatively affected economic growth in the short term.