Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.

Kationinvaihtohartsien hapetuskestävyys

Hyvin puhdasta vettä vaativissa sovelluksissa käytettävät kationinvaihtohartsit eivät saisi vuotaa puhdistettavaan veteen mitään vieraita aineita. Todellisuudessa hartsit kuitenkin vuotavat hyvin pieniä määriä erilaisia yhdisteitä käytön aikana. Aineet, joita kationinvaihtohartsi päästää veteen, ovat osaksi hartsin polymerointireaktion aikana sen rungon sisään jääneitä yhdisteitä. Nämä voidaan suurimmaksi osaksi poistaa pesemällä hartsia. Osittain niitä syntyy myös hartsin polystyreenidivinyylibentseenirungon (PS-DVB) hapettuessa. Hapettumisen seurauksena syntyneet yhdisteet ovat pääosin orgaanisia sulfonaatteja. Tämä työ koskee ydinvoimalaitoksissa käytettäviä pulverihartseja, joita käytetään primääripiirissä kiertävän lauhdeveden puhdistukseen ja jotka joutuvat siellä alttiiksi hapettumiselle. Yleensä hapettuminen on hidasta ja se johtuu veteen liuenneesta hapesta. Hapettuminen nopeutuu huomattavasti, jos vedessä on läsnä hapettimia tai siirtymämetalli-ioneja. Tällaisia hapettimia ovat esimerkiksi vetyperoksidi, otsoni, vapaa kloori, typpihappo ja kromi. Vetyperoksidin vaikutuksesta hartsin runkoon muodostuu hydroperoksidiryhmä, jonka hajoamisesta alkaa reaktioiden sarja, joka lopulta johtaa hartsin polymeerirungon katkeamiseen. Siirtymämetalli-ionit katalysoivat peroksidien hajoamista. Tavallisimpia hapetusta katalysoivia metalli-ioneja ovat rauta ja kupari, joiden katalyyttinen aktiivisuus on suuri. Tässä työssä pyrittiin selvittämään, onko mahdollista valmistaa hartseja, jotka kestävät hapettumista paremmin kuin nykyisin käytössä olevat hartsit. Sen tutkimiseksi tehtiin kiihdytettyjä hapetuskokeita käyttäen hapettimena vetyperoksidia ilman siirtymämetalli-ioni katalyyttejä. Hapetuskokeet tehtiin kaupallisesti saatavilla hartseilla ja uusilla työtä varten syntetisoiduilla koehartseilla. Hapetuskokeiden etenemistä seurattiin mittaamalla veteen liuenneiden orgaanisten aineiden kokonaismäärää (TOC-analyysi) ja liuoksessa esiintyvien orgaanisten sulfonaattien määrää johtokykymittauksin. Saadut tulokset antoivat viitteitä siitä, että hartsin synteesiolosuhteilla voi olla suurempi vaikutus sen hapetuskestävyyteen kuin synteesissä käytetyillä raaka-aineilla.

Time-varying Risk Premiums and Conditional Market Risk: Empirical Evidence from European Stock Markets

This study investigates the relationship between the time-varying risk premiums and conditional market risk in the stock markets of the ten member countries of Economy and Monetary Union. Second, it examines whether the conditional second moments change over time and are there asymmetric effects in the conditional covariance matrix. Third, it analyzes the possible effects of the chosen testing framework. Empirical analysis is conducted using asymmetric univariate and multivariate GARCH-in-mean models and assuming three different degrees of market integration. For a daily sample period from 1999 to 2007, the study shows that the time-varying market risk alone is not enough to explain the dynamics of risk premiums and indications are found that the market risk is detected only when its price is allowed to change over time. Also asymmetric effects in the conditional covariance matrix, which is found to be time-varying, are clearly present and should be recognized in empirical asset pricing analyses.

On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Inverting ionospheric D-region electron density pro-file from riometer measurement

The aim of this work is to invert the ionospheric electron density profile from Riometer (Relative Ionospheric opacity meter) measurement. The newly Riometer instrument KAIRA (Kilpisjärvi Atmospheric Imaging Receiver Array) is used to measure the cosmic HF radio noise absorption that taking place in the D-region ionosphere between 50 to 90 km. In order to invert the electron density profile synthetic data is used to feed the unknown parameter Neq using spline height method, which works by taking electron density profile at different altitude. Moreover, smoothing prior method also used to sample from the posterior distribution by truncating the prior covariance matrix. The smoothing profile approach makes the problem easier to find the posterior using MCMC (Markov Chain Monte Carlo) method.

Variational Ensemble Kalman Filtering in Hydrology

The current thesis manuscript studies the suitability of a recent data assimilation method, the Variational Ensemble Kalman Filter (VEnKF), to real-life fluid dynamic problems in hydrology. VEnKF combines a variational formulation of the data assimilation problem based on minimizing an energy functional with an Ensemble Kalman filter approximation to the Hessian matrix that also serves as an approximation to the inverse of the error covariance matrix. One of the significant features of VEnKF is the very frequent re-sampling of the ensemble: resampling is done at every observation step. This unusual feature is further exacerbated by observation interpolation that is seen beneficial for numerical stability. In this case the ensemble is resampled every time step of the numerical model. VEnKF is implemented in several configurations to data from a real laboratory-scale dam break problem modelled with the shallow water equations. It is also tried in a two-layer Quasi- Geostrophic atmospheric flow problem. In both cases VEnKF proves to be an efficient and accurate data assimilation method that renders the analysis more realistic than the numerical model alone. It also proves to be robust against filter instability by its adaptive nature.

Bayesian analysis of SEIR epidemic models

This thesis concerns the analysis of epidemic models. We adopt the Bayesian paradigm and develop suitable Markov Chain Monte Carlo (MCMC) algorithms. This is done by considering an Ebola outbreak in the Democratic Republic of Congo, former Zaïre, 1995 as a case of SEIR epidemic models. We model the Ebola epidemic deterministically using ODEs and stochastically through SDEs to take into account a possible bias in each compartment. Since the model has unknown parameters, we use different methods to estimate them such as least squares, maximum likelihood and MCMC. The motivation behind choosing MCMC over other existing methods in this thesis is that it has the ability to tackle complicated nonlinear problems with large number of parameters. First, in a deterministic Ebola model, we compute the likelihood function by sum of square of residuals method and estimate parameters using the LSQ and MCMC methods. We sample parameters and then use them to calculate the basic reproduction number and to study the disease-free equilibrium. From the sampled chain from the posterior, we test the convergence diagnostic and confirm the viability of the model. The results show that the Ebola model fits the observed onset data with high precision, and all the unknown model parameters are well identified. Second, we convert the ODE model into a SDE Ebola model. We compute the likelihood function using extended Kalman filter (EKF) and estimate parameters again. The motivation of using the SDE formulation here is to consider the impact of modelling errors. Moreover, the EKF approach allows us to formulate a filtered likelihood for the parameters of such a stochastic model. We use the MCMC procedure to attain the posterior distributions of the parameters of the SDE Ebola model drift and diffusion parts. In this thesis, we analyse two cases: (1) the model error covariance matrix of the dynamic noise is close to zero , i.e. only small stochasticity added into the model. The results are then similar to the ones got from deterministic Ebola model, even if methods of computing the likelihood function are different (2) the model error covariance matrix is different from zero, i.e. a considerable stochasticity is introduced into the Ebola model. This accounts for the situation where we would know that the model is not exact. As a results, we obtain parameter posteriors with larger variances. Consequently, the model predictions then show larger uncertainties, in accordance with the assumption of an incomplete model.

Static waves in corporate space : characterizing oscillating trading patterns in New York stock exchange

Various researches in the field of econophysics has shown that fluid flow have analogous phenomena in financial market behavior, the typical parallelism being delivered between energy in fluids and information on markets. However, the geometry of the manifold on which market dynamics act out their dynamics (corporate space) is not yet known. In this thesis, utilizing a Seven year time series of prices of stocks used to compute S&P500 index on the New York Stock Exchange, we have created local chart to the corporate space with the goal of finding standing waves and other soliton like patterns in the behavior of stock price deviations from the S&P500 index. By first calculating the correlation matrix of normalized stock price deviations from the S&P500 index, we have performed a local singular value decomposition over a set of four different time windows as guides to the nature of patterns that may emerge. I turns out that in almost all cases, each singular vector is essentially determined by relatively small set of companies with big positive or negative weights on that singular vector. Over particular time windows, sometimes these weights are strongly correlated with at least one industrial sector and certain sectors are more prone to fast dynamics whereas others have longer standing waves.

Modeling Forest Growth with Management Data: A Matrix Approach for the Italian Alps

Summary

Matrix Analytic Analysis of Delays in Communication Systems

Tässä päättötyössä annetaan kuvaus kehitetystä sovelluksesta Quasi Birth Death processien ratkaisuun. Tämä ohjelma on tähän mennessä ainutlaatuinen ja sen avulla voi ratkaista sarjan tehtäviä ja sitä tarvitaan kommunikaatio systeemien analyysiin. Mainittuun sovellukseen on annettu kuvaus ja määritelmä. Lyhyt kuvaus toisesta sovelluksesta Quasi Birth Death prosessien tehtävien ratkaisuun on myös annettu