An application of a physically based SOIL model to the Bowen ratio data

Yhteenveto: Haihdunnan mittaamisesta ja mallintamisesta peltoalueella

SU-8-Based Microchips for Capillary Electrophoresis and Electrospray Ionization Mass Spectrometry

Miniaturization of analytical instrumentation is attracting growing interest in response to the explosive demand for rapid, yet sensitive analytical methods and low-cost, highly automated instruments for pharmaceutical and bioanalyses and environmental monitoring. Microfabrication technology in particular, has enabled fabrication of low-cost microdevices with a high degree of integrated functions, such as sample preparation, chemical reaction, separation, and detection, on a single microchip. These miniaturized total chemical analysis systems (microTAS or lab-on-a-chip) can also be arrayed for parallel analyses in order to accelerate the sample throughput. Other motivations include reduced sample consumption and waste production as well as increased speed of analysis. One of the most promising hyphenated techniques in analytical chemistry is the combination of a microfluidic separation chip and mass spectrometer (MS). In this work, the emerging polymer microfabrication techniques, ultraviolet lithography in particular, were exploited to develop a capillary electrophoresis (CE) separation chip which incorporates a monolithically integrated electrospray ionization (ESI) emitter for efficient coupling with MS. An epoxy photoresist SU-8 was adopted as structural material and characterized with respect to its physicochemical properties relevant to chip-based CE and ESI/MS, namely surface charge, surface interactions, heat transfer, and solvent compatibility. As a result, SU-8 was found to be a favorable material to substitute for the more commonly used glass and silicon in microfluidic applications. In addition, an infrared (IR) thermography was introduced as direct, non-intrusive method to examine the heat transfer and thermal gradients during microchip-CE. The IR data was validated through numerical modeling. The analytical performance of SU-8-based microchips was established for qualitative and quantitative CE-ESI/MS analysis of small drug compounds, peptides, and proteins. The CE separation efficiency was found to be similar to that of commercial glass microchips and conventional CE systems. Typical analysis times were only 30-90 s per sample indicating feasibility for high-throughput analysis. Moreover, a mass detection limit at the low-attomole level, as low as 10E+5 molecules, was achieved utilizing MS detection. The SU-8 microchips developed in this work could also be mass produced at low cost and with nearly identical performance from chip to chip. Until this work, the attempts to combine CE separation with ESI in a chip-based system, amenable to batch fabrication and capable of high, reproducible analytical performance, have not been successful. Thus, the CE-ESI chip developed in this work is a substantial step toward lab-on-a-chip technology.

Univariate, bivariate, and multivariate methods in corpus-based lexicography : A study of synonymy

In this dissertation, I present an overall methodological framework for studying linguistic alternations, focusing specifically on lexical variation in denoting a single meaning, that is, synonymy. As the practical example, I employ the synonymous set of the four most common Finnish verbs denoting THINK, namely ajatella, miettiä, pohtia and harkita ‘think, reflect, ponder, consider’. As a continuation to previous work, I describe in considerable detail the extension of statistical methods from dichotomous linguistic settings (e.g., Gries 2003; Bresnan et al. 2007) to polytomous ones, that is, concerning more than two possible alternative outcomes. The applied statistical methods are arranged into a succession of stages with increasing complexity, proceeding from univariate via bivariate to multivariate techniques in the end. As the central multivariate method, I argue for the use of polytomous logistic regression and demonstrate its practical implementation to the studied phenomenon, thus extending the work by Bresnan et al. (2007), who applied simple (binary) logistic regression to a dichotomous structural alternation in English. The results of the various statistical analyses confirm that a wide range of contextual features across different categories are indeed associated with the use and selection of the selected think lexemes; however, a substantial part of these features are not exemplified in current Finnish lexicographical descriptions. The multivariate analysis results indicate that the semantic classifications of syntactic argument types are on the average the most distinctive feature category, followed by overall semantic characterizations of the verb chains, and then syntactic argument types alone, with morphological features pertaining to the verb chain and extra-linguistic features relegated to the last position. In terms of overall performance of the multivariate analysis and modeling, the prediction accuracy seems to reach a ceiling at a Recall rate of roughly two-thirds of the sentences in the research corpus. The analysis of these results suggests a limit to what can be explained and determined within the immediate sentential context and applying the conventional descriptive and analytical apparatus based on currently available linguistic theories and models. The results also support Bresnan’s (2007) and others’ (e.g., Bod et al. 2003) probabilistic view of the relationship between linguistic usage and the underlying linguistic system, in which only a minority of linguistic choices are categorical, given the known context – represented as a feature cluster – that can be analytically grasped and identified. Instead, most contexts exhibit degrees of variation as to their outcomes, resulting in proportionate choices over longer stretches of usage in texts or speech.

On probability-based inference under data missing by design

Whether a statistician wants to complement a probability model for observed data with a prior distribution and carry out fully probabilistic inference, or base the inference only on the likelihood function, may be a fundamental question in theory, but in practice it may well be of less importance if the likelihood contains much more information than the prior. Maximum likelihood inference can be justified as a Gaussian approximation at the posterior mode, using flat priors. However, in situations where parametric assumptions in standard statistical models would be too rigid, more flexible model formulation, combined with fully probabilistic inference, can be achieved using hierarchical Bayesian parametrization. This work includes five articles, all of which apply probability modeling under various problems involving incomplete observation. Three of the papers apply maximum likelihood estimation and two of them hierarchical Bayesian modeling. Because maximum likelihood may be presented as a special case of Bayesian inference, but not the other way round, in the introductory part of this work we present a framework for probability-based inference using only Bayesian concepts. We also re-derive some results presented in the original articles using the toolbox equipped herein, to show that they are also justifiable under this more general framework. Here the assumption of exchangeability and de Finetti's representation theorem are applied repeatedly for justifying the use of standard parametric probability models with conditionally independent likelihood contributions. It is argued that this same reasoning can be applied also under sampling from a finite population. The main emphasis here is in probability-based inference under incomplete observation due to study design. This is illustrated using a generic two-phase cohort sampling design as an example. The alternative approaches presented for analysis of such a design are full likelihood, which utilizes all observed information, and conditional likelihood, which is restricted to a completely observed set, conditioning on the rule that generated that set. Conditional likelihood inference is also applied for a joint analysis of prevalence and incidence data, a situation subject to both left censoring and left truncation. Other topics covered are model uncertainty and causal inference using posterior predictive distributions. We formulate a non-parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure, and apply the model in the context of optimal sequential treatment regimes, demonstrating that inference based on posterior predictive distributions is feasible also in this case.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Modeling ecological and evolutionary processes in spatially structured populations

Many species inhabit fragmented landscapes, resulting either from anthropogenic or from natural processes. The ecological and evolutionary dynamics of spatially structured populations are affected by a complex interplay between endogenous and exogenous factors. The metapopulation approach, simplifying the landscape to a discrete set of patches of breeding habitat surrounded by unsuitable matrix, has become a widely applied paradigm for the study of species inhabiting highly fragmented landscapes. In this thesis, I focus on the construction of biologically realistic models and their parameterization with empirical data, with the general objective of understanding how the interactions between individuals and their spatially structured environment affect ecological and evolutionary processes in fragmented landscapes. I study two hierarchically structured model systems, which are the Glanville fritillary butterfly in the Åland Islands, and a system of two interacting aphid species in the Tvärminne archipelago, both being located in South-Western Finland. The interesting and challenging feature of both study systems is that the population dynamics occur over multiple spatial scales that are linked by various processes. My main emphasis is in the development of mathematical and statistical methodologies. For the Glanville fritillary case study, I first build a Bayesian framework for the estimation of death rates and capture probabilities from mark-recapture data, with the novelty of accounting for variation among individuals in capture probabilities and survival. I then characterize the dispersal phase of the butterflies by deriving a mathematical approximation of a diffusion-based movement model applied to a network of patches. I use the movement model as a building block to construct an individual-based evolutionary model for the Glanville fritillary butterfly metapopulation. I parameterize the evolutionary model using a pattern-oriented approach, and use it to study how the landscape structure affects the evolution of dispersal. For the aphid case study, I develop a Bayesian model of hierarchical multi-scale metapopulation dynamics, where the observed extinction and colonization rates are decomposed into intrinsic rates operating specifically at each spatial scale. In summary, I show how analytical approaches, hierarchical Bayesian methods and individual-based simulations can be used individually or in combination to tackle complex problems from many different viewpoints. In particular, hierarchical Bayesian methods provide a useful tool for decomposing ecological complexity into more tractable components.

Optical Studies of the Antarctic Glacio-Oceanic System

The Antarctic system comprises of the continent itself, Antarctica, and the ocean surrounding it, the Southern Ocean. The system has an important part in the global climate due to its size, its high latitude location and the negative radiation balance of its large ice sheets. Antarctica has also been in focus for several decades due to increased ultraviolet (UV) levels caused by stratospheric ozone depletion, and the disintegration of its ice shelves. In this study, measurements were made during three Austral summers to study the optical properties of the Antarctic system and to produce radiation information for additional modeling studies. These are related to specific phenomena found in the system. During the summer of 1997-1998, measurements of beam absorption and beam attenuation coefficients, and downwelling and upwelling irradiance were made in the Southern Ocean along a S-N transect at 6°E. The attenuation of photosynthetically active radiation (PAR) was calculated and used together with hydrographic measurements to judge whether the phytoplankton in the investigated areas of the Southern Ocean are light limited. By using the Kirk formula the diffuse attenuation coefficient was linked to the absorption and scattering coefficients. The diffuse attenuation coefficients (Kpar) for PAR were found to vary between 0.03 and 0.09 1/m. Using the values for KPAR and the definition of the Sverdrup critical depth, the studied Southern Ocean plankton systems were found not to be light limited. Variabilities in the spectral and total albedo of snow were studied in the Queen Maud Land region of Antarctica during the summers of 1999-2000 and 2000-2001. The measurement areas were the vicinity of the South African Antarctic research station SANAE 4, and a traverse near the Finnish Antarctic research station Aboa. The midday mean total albedos for snow were between 0.83, for clear skies, and 0.86, for overcast skies, at Aboa and between 0.81 and 0.83 for SANAE 4. The mean spectral albedo levels at Aboa and SANAE 4 were very close to each other. The variations in the spectral albedos were due more to differences in ambient conditions than variations in snow properties. A Monte-Carlo model was developed to study the spectral albedo and to develop a novel nondestructive method to measure the diffuse attenuation coefficient of snow. The method was based on the decay of upwelling radiation moving horizontally away from a source of downwelling light. This was assumed to have a relation to the diffuse attenuation coefficient. In the model, the attenuation coefficient obtained from the upwelling irradiance was higher than that obtained using vertical profiles of downwelling irradiance. The model results were compared to field measurements made on dry snow in Finnish Lapland and they correlated reasonably well. Low-elevation (below 1000 m) blue-ice areas may experience substantial melt-freeze cycles due to absorbed solar radiation and the small heat conductivity in the ice. A two-dimensional (x-z) model has been developed to simulate the formation and water circulation in the subsurface ponds. The model results show that for a physically reasonable parameter set the formation of liquid water within the ice can be reproduced. The results however are sensitive to the chosen parameter values, and their exact values are not well known. Vertical convection and a weak overturning circulation is generated stratifying the fluid and transporting warmer water downward, thereby causing additional melting at the base of the pond. In a 50-year integration, a global warming scenario mimicked by a decadal scale increase of 3 degrees per 100 years in air temperature, leads to a general increase in subsurface water volume. The ice did not disintegrate due to the air temperature increase after the 50 year integration.

Theoretical modeling of ionospheric electrodynamics including induction effects

This thesis deals with theoretical modeling of the electrodynamics of auroral ionospheres. In the five research articles forming the main part of the thesis we have concentrated on two main themes: Development of new data-analysis techniques and study of inductive phenomena in the ionospheric electrodynamics. The introductory part of the thesis provides a background for these new results and places them in the wider context of ionospheric research. In this thesis we have developed a new tool (called 1D SECS) for analysing ground based magnetic measurements from a 1-dimensional magnetometer chain (usually aligned in the North-South direction) and a new method for obtaining ionospheric electric field from combined ground based magnetic measurements and estimated ionospheric electric conductance. Both these methods are based on earlier work, but contain important new features: 1D SECS respects the spherical geometry of large scale ionospheric electrojet systems and due to an innovative way of implementing boundary conditions the new method for obtaining electric fields can be applied also at local scale studies. These new calculation methods have been tested using both simulated and real data. The tests indicate that the new methods are more reliable than the previous techniques. Inductive phenomena are intimately related to temporal changes in electric currents. As the large scale ionospheric current systems change relatively slowly, in time scales of several minutes or hours, inductive effects are usually assumed to be negligible. However, during the past ten years, it has been realised that induction can play an important part in some ionospheric phenomena. In this thesis we have studied the role of inductive electric fields and currents in ionospheric electrodynamics. We have formulated the induction problem so that only ionospheric electric parameters are used in the calculations. This is in contrast to previous studies, which require knowledge of the magnetospheric-ionosphere coupling. We have applied our technique to several realistic models of typical auroral phenomena. The results indicate that inductive electric fields and currents are locally important during the most dynamical phenomena (like the westward travelling surge, WTS). In these situations induction may locally contribute up to 20-30% of the total ionospheric electric field and currents. Inductive phenomena do also change the field-aligned currents flowing between the ionosphere and magnetosphere, thus modifying the coupling between the two regions.

Modeling of Surface UV Radiation Using Satellite Data

Solar UV radiation is harmful for life on planet Earth, but fortunately the atmospheric oxygen and ozone absorb almost entirely the most energetic UVC radiation photons. However, part of the UVB radiation and much of the UVA radiation reaches the surface of the Earth, and affect human health, environment, materials and drive atmospheric and aquatic photochemical processes. In order to quantify these effects and processes there is a need for ground-based UV measurements and radiative transfer modeling to estimate the amounts of UV radiation reaching the biosphere. Satellite measurements with their near-global spatial coverage and long-term data conti-nuity offer an attractive option for estimation of the surface UV radiation. This work focuses on radiative transfer theory based methods used for estimation of the UV radiation reaching the surface of the Earth. The objectives of the thesis were to implement the surface UV algorithm originally developed at NASA Goddard Space Flight Center for estimation of the surface UV irradiance from the meas-urements of the Dutch-Finnish built Ozone Monitoring Instrument (OMI), to improve the original surface UV algorithm especially in relation with snow cover, to validate the OMI-derived daily surface UV doses against ground-based measurements, and to demonstrate how the satellite-derived surface UV data can be used to study the effects of the UV radiation. The thesis consists of seven original papers and a summary. The summary includes an introduction of the OMI instrument, a review of the methods used for modeling of the surface UV using satellite data as well as the con-clusions of the main results of the original papers. The first two papers describe the algorithm used for estimation of the surface UV amounts from the OMI measurements as well as the unique Very Fast Delivery processing system developed for processing of the OMI data received at the Sodankylä satellite data centre. The third and the fourth papers present algorithm improvements related to the surface UV albedo of the snow-covered land. Fifth paper presents the results of the comparison of the OMI-derived daily erythemal doses with those calculated from the ground-based measurement data. It gives an estimate of the expected accuracy of the OMI-derived sur-face UV doses for various atmospheric and other conditions, and discusses the causes of the differences between the satellite-derived and ground-based data. The last two papers demonstrate the use of the satellite-derived sur-face UV data. Sixth paper presents an assessment of the photochemical decomposition rates in aquatic environment. Seventh paper presents use of satellite-derived daily surface UV doses for planning of the outdoor material weathering tests.

11β-Hydroxysteroid dehydrogenase inhibitors and selectivity modeling of 11β-HSDs

11β-hydroksisteroididehydrogenaasientsyymit (11β-HSD) 1 ja 2 säätelevät kortisonin ja kortisolin määrää kudoksissa. 11β-HSD1 -entsyymin ylimäärä erityisesti viskeraalisessa rasvakudoksessa aiheuttaa metaboliseen oireyhtymän klassisia oireita, mikä tarjoaa mahdollisuuden metabolisen oireyhtymän hoitoon 11β-HSD1 -entsyymin selektiivisellä estämisellä. 11β-HSD2 -entsyymin inhibitio aiheuttaa kortisonivälitteisen mineralokortikoidireseptorien aktivoitumisen, mikä puolestaan johtaa hypertensiivisiin haittavaikutuksiin. Haittavaikutuksista huolimatta 11β-HSD2 -entsyymin estäminen saattaa olla hyödyllistä tilanteissa, joissa halutaan nostaa kortisolin määrä elimistössä. Lukuisia selektiivisiä 11β-HSD1 inhibiittoreita on kehitetty, mutta 11β-HSD2-inhibiittoreita on raportoitu vähemmän. Ero näiden kahden isotsyymin aktiivisen kohdan välillä on myös tuntematon, mikä vaikeuttaa selektiivisten inhibiittoreiden kehittämistä kummallekin entsyymille. Tällä työllä oli kaksi tarkoitusta: (1) löytää ero 11β-HSD entsyymien välillä ja (2) kehittää farmakoforimalli, jota voitaisiin käyttää selektiivisten 11β-HSD2 -inhibiittoreiden virtuaaliseulontaan. Ongelmaa lähestyttiin tietokoneavusteisesti: homologimallinnuksella, pienmolekyylien telakoinnilla proteiiniin, ligandipohjaisella farmakoforimallinnuksella ja virtuaaliseulonnalla. Homologimallinnukseen käytettiin SwissModeler -ohjelmaa, ja luotu malli oli hyvin päällekäinaseteltavissa niin templaattinsa (17β-HSD1) kuin 11β-HSD1 -entsyymin kanssa. Eroa entsyymien välillä ei löytynyt tarkastelemalla päällekäinaseteltuja entsyymejä. Seitsemän yhdistettä, joista kuusi on 11β-HSD2 -selektiivisiä, telakoitiin molempiin entsyymeihin käyttäen ohjelmaa GOLD. 11β-HSD1 -entsyymiin yhdisteet kiinnittyivät kuten suurin osa 11β-HSD1 -selektiivisistä tai epäselektiivisistä inhibiittoreista, kun taas 11β-HSD2 -entsyymiin kaikki yhdisteet olivat telakoituneet käänteisesti. Tällainen sitoutumistapa mahdollistaa vetysidokset Ser310:een ja Asn171:een, aminohappoihin, jotka olivat nähtävissä vain 11β-HSD2 -entsyymissä. Farmakoforimallinnukseen käytettiin ohjelmaa LigandScout3.0, jolla ajettiin myös virtuaaliseulonnat. Luodut kaksi farmakoforimallia, jotka perustuivat aiemmin telakointiinkin käytettyihin kuuteen 11β-HSD2 -selektiiviseen yhdisteeseen, koostuivat kuudesta ominaisuudesta (vetysidosakseptori, vetysidosdonori ja hydrofobinen), ja kieltoalueista. 11β-HSD2 -selektiivisyyden kannalta tärkeimmät ominaisuudet ovat vetysidosakseptori, joka voi muodostaa sidoksen Ser310 kanssa ja vetysidosdonori sen vieressä. Tälle vetysidosdonorille ei löytynyt vuorovaikutusparia 11β-HSD2-mallista. Sopivasti proteiiniin orientoitunut vesimolekyyli voisi kuitenkin olla sopiva ratkaisu puuttuvalle vuorovaikutusparille. Koska molemmat farmakoforimallit löysivät 11β-HSD2 -selektiivisiä yhdisteitä ja jättivät epäselektiivisiä pois testiseulonnassa, käytettiin molempia malleja Innsbruckin yliopistossa säilytettävistä yhdisteistä (2700 kappaletta) koostetun tietokannan seulontaan. Molemmista seulonnoista löytyneistä hiteistä valittiin yhteensä kymmenen kappaletta, jotka lähetettiin biologisiin testeihin. Biologisien testien tulokset vahvistavat lopullisesti sen kuinka hyvin luodut mallit edustavat todellisuudessa 11β-HSD2 -selektiivisyyttä.

Essays on the Modeling and Prediction of Volatility and Higher Moments of Stock Returns (summary section only)

One of the most fundamental and widely accepted ideas in finance is that investors are compensated through higher returns for taking on non-diversifiable risk. Hence the quantification, modeling and prediction of risk have been, and still are one of the most prolific research areas in financial economics. It was recognized early on that there are predictable patterns in the variance of speculative prices. Later research has shown that there may also be systematic variation in the skewness and kurtosis of financial returns. Lacking in the literature so far, is an out-of-sample forecast evaluation of the potential benefits of these new more complicated models with time-varying higher moments. Such an evaluation is the topic of this dissertation. Essay 1 investigates the forecast performance of the GARCH (1,1) model when estimated with 9 different error distributions on Standard and Poor’s 500 Index Future returns. By utilizing the theory of realized variance to construct an appropriate ex post measure of variance from intra-day data it is shown that allowing for a leptokurtic error distribution leads to significant improvements in variance forecasts compared to using the normal distribution. This result holds for daily, weekly as well as monthly forecast horizons. It is also found that allowing for skewness and time variation in the higher moments of the distribution does not further improve forecasts. In Essay 2, by using 20 years of daily Standard and Poor 500 index returns, it is found that density forecasts are much improved by allowing for constant excess kurtosis but not improved by allowing for skewness. By allowing the kurtosis and skewness to be time varying the density forecasts are not further improved but on the contrary made slightly worse. In Essay 3 a new model incorporating conditional variance, skewness and kurtosis based on the Normal Inverse Gaussian (NIG) distribution is proposed. The new model and two previously used NIG models are evaluated by their Value at Risk (VaR) forecasts on a long series of daily Standard and Poor’s 500 returns. The results show that only the new model produces satisfactory VaR forecasts for both 1% and 5% VaR Taken together the results of the thesis show that kurtosis appears not to exhibit predictable time variation, whereas there is found some predictability in the skewness. However, the dynamic properties of the skewness are not completely captured by any of the models.

Essays on Risk Modeling. Applications to Portfolio and Risk Management (summary section only)

In this thesis we deal with the concept of risk. The objective is to bring together and conclude on some normative information regarding quantitative portfolio management and risk assessment. The first essay concentrates on return dependency. We propose an algorithm for classifying markets into rising and falling. Given the algorithm, we derive a statistic: the Trend Switch Probability, for detection of long-term return dependency in the first moment. The empirical results suggest that the Trend Switch Probability is robust over various volatility specifications. The serial dependency in bear and bull markets behaves however differently. It is strongly positive in rising market whereas in bear markets it is closer to a random walk. Realized volatility, a technique for estimating volatility from high frequency data, is investigated in essays two and three. In the second essay we find, when measuring realized variance on a set of German stocks, that the second moment dependency structure is highly unstable and changes randomly. Results also suggest that volatility is non-stationary from time to time. In the third essay we examine the impact from market microstructure on the error between estimated realized volatility and the volatility of the underlying process. With simulation-based techniques we show that autocorrelation in returns leads to biased variance estimates and that lower sampling frequency and non-constant volatility increases the error variation between the estimated variance and the variance of the underlying process. From these essays we can conclude that volatility is not easily estimated, even from high frequency data. It is neither very well behaved in terms of stability nor dependency over time. Based on these observations, we would recommend the use of simple, transparent methods that are likely to be more robust over differing volatility regimes than models with a complex parameter universe. In analyzing long-term return dependency in the first moment we find that the Trend Switch Probability is a robust estimator. This is an interesting area for further research, with important implications for active asset allocation.