An Empirical Comparison of Linear and Nonlinear Volatility Models for Nordic Stock Returns

This paper examines how volatility in financial markets can preferable be modeled. The examination investigates how good the models for the volatility, both linear and nonlinear, are in absorbing skewness and kurtosis. The examination is done on the Nordic stock markets, including Finland, Sweden, Norway and Denmark. Different linear and nonlinear models are applied, and the results indicates that a linear model can almost always be used for modeling the series under investigation, even though nonlinear models performs slightly better in some cases. These results indicate that the markets under study are exposed to asymmetric patterns only to a certain degree. Negative shocks generally have a more prominent effect on the markets, but these effects are not really strong. However, in terms of absorbing skewness and kurtosis, nonlinear models outperform linear ones.

Effects of environmental variation on ecological and evolutionary dynamics

Environmental variation is a fact of life for all the species on earth: for any population of any particular species, the local environmental conditions are liable to vary in both time and space. In today's world, anthropogenic activity is causing habitat loss and fragmentation for many species, which may profoundly alter the characteristics of environmental variation in remaining habitat. Previous research indicates that, as habitat is lost, the spatial configuration of remaining habitat will increasingly affect the dynamics by which populations are governed. Through the use of mathematical models, this thesis asks how environmental variation interacts with species properties to influence population dynamics, local adaptation, and dispersal evolution. More specifically, we couple continuous-time continuous-space stochastic population dynamic models to landscape models. We manipulate environmental variation via parameters such as mean patch size, patch density, and patch longevity. Among other findings, we show that a mixture of high and low quality habitat is commonly better for a population than uniformly mediocre habitat. This conclusion is justified by purely ecological arguments, yet the positive effects of landscape heterogeneity may be enhanced further by local adaptation, and by the evolution of short-ranged dispersal. The predicted evolutionary responses to environmental variation are complex, however, since they involve numerous conflicting factors. We discuss why the species that have high levels of local adaptation within their ranges may not be the same species that benefit from local adaptation during range expansion. We show how habitat loss can lead to either increased or decreased selection for dispersal depending on the type of habitat and the manner in which it is lost. To study the models, we develop a recent analytical method, Perturbation expansion, to enable the incorporation of environmental variation. Within this context, we use two methods to address evolutionary dynamics: Adaptive dynamics, which assumes mutations occur infrequently so that the ecological and evolutionary timescales can be separated, and via Genotype distributions, which assume mutations are more frequent. The two approaches generally lead to similar predictions yet, exceptionally, we show how the evolutionary response of dispersal behaviour to habitat turnover may qualitatively depend on the mutation rate.

Bootstrapping the Error Correction Model Cointegration Test

This paper is concerned with using the bootstrap to obtain improved critical values for the error correction model (ECM) cointegration test in dynamic models. In the paper we investigate the effects of dynamic specification on the size and power of the ECM cointegration test with bootstrap critical values. The results from a Monte Carlo study show that the size of the bootstrap ECM cointegration test is close to the nominal significance level. We find that overspecification of the lag length results in a loss of power. Underspecification of the lag length results in size distortion. The performance of the bootstrap ECM cointegration test deteriorates if the correct lag length is not used in the ECM. The bootstrap ECM cointegration test is therefore not robust to model misspecification.

Diagnostic Tests Based on Quantile Residuals for Nonlinear Time Series Models

This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

Dynamic Factor Models and Forecasting Finnish Macroeconomic Variables

In recent years, thanks to developments in information technology, large-dimensional datasets have been increasingly available. Researchers now have access to thousands of economic series and the information contained in them can be used to create accurate forecasts and to test economic theories. To exploit this large amount of information, researchers and policymakers need an appropriate econometric model.Usual time series models, vector autoregression for example, cannot incorporate more than a few variables. There are two ways to solve this problem: use variable selection procedures or gather the information contained in the series to create an index model. This thesis focuses on one of the most widespread index model, the dynamic factor model (the theory behind this model, based on previous literature, is the core of the first part of this study), and its use in forecasting Finnish macroeconomic indicators (which is the focus of the second part of the thesis). In particular, I forecast economic activity indicators (e.g. GDP) and price indicators (e.g. consumer price index), from 3 large Finnish datasets. The first dataset contains a large series of aggregated data obtained from the Statistics Finland database. The second dataset is composed by economic indicators from Bank of Finland. The last dataset is formed by disaggregated data from Statistic Finland, which I call micro dataset. The forecasts are computed following a two steps procedure: in the first step I estimate a set of common factors from the original dataset. The second step consists in formulating forecasting equations including the factors extracted previously. The predictions are evaluated using relative mean squared forecast error, where the benchmark model is a univariate autoregressive model. The results are dataset-dependent. The forecasts based on factor models are very accurate for the first dataset (the Statistics Finland one), while they are considerably worse for the Bank of Finland dataset. The forecasts derived from the micro dataset are still good, but less accurate than the ones obtained in the first case. This work leads to multiple research developments. The results here obtained can be replicated for longer datasets. The non-aggregated data can be represented in an even more disaggregated form (firm level). Finally, the use of the micro data, one of the major contributions of this thesis, can be useful in the imputation of missing values and the creation of flash estimates of macroeconomic indicator (nowcasting).

Oxidative stability of phytosterols in food models and foods

An important safety aspect to be considered when foods are enriched with phytosterols and phytostanols is the oxidative stability of these lipid compounds, i.e. their resistance to oxidation and thus to the formation of oxidation products. This study concentrated on producing scientific data to support this safety evaluation process. In the absence of an official method for analyzing of phytosterol/stanol oxidation products, we first developed a new gas chromatographic - mass spectrometric (GC-MS) method. We then investigated factors affecting these compounds' oxidative stability in lipid-based food models in order to identify critical conditions under which significant oxidation reactions may occur. Finally, the oxidative stability of phytosterols and stanols in enriched foods during processing and storage was evaluated. Enriched foods covered a range of commercially available phytosterol/stanol ingredients, different heat treatments during food processing, and different multiphase food structures. The GC-MS method was a powerful tool for measuring the oxidative stability. Data obtained in food model studies revealed that the critical factors for the formation and distribution of the main secondary oxidation products were sterol structure, reaction temperature, reaction time, and lipid matrix composition. Under all conditions studied, phytostanols as saturated compounds were more stable than unsaturated phytosterols. In addition, esterification made phytosterols more reactive than free sterols at low temperatures, while at high temperatures the situation was the reverse. Generally, oxidation reactions were more significant at temperatures above 100°C. At lower temperatures, the significance of these reactions increased with increasing reaction time. The effect of lipid matrix composition was dependent on temperature; at temperatures above 140°C, phytosterols were more stable in an unsaturated lipid matrix, whereas below 140°C they were more stable in a saturated lipid matrix. At 140°C, phytosterols oxidized at the same rate in both matrices. Regardless of temperature, phytostanols oxidized more in an unsaturated lipid matrix. Generally, the distribution of oxidation products seemed to be associated with the phase of overall oxidation. 7-ketophytosterols accumulated when oxidation had not yet reached the dynamic state. Once this state was attained, the major products were 5,6-epoxyphytosterols and 7-hydroxyphytosterols. The changes observed in phytostanol oxidation products were not as informative since all stanol oxides quantified represented hydroxyl compounds. The formation of these secondary oxidation products did not account for all of the phytosterol/stanol losses observed during the heating experiments, indicating the presence of dimeric, oligomeric or other oxidation products, especially when free phytosterols and stanols were heated at high temperatures. Commercially available phytosterol/stanol ingredients were stable during such food processes as spray-drying and ultra high temperature (UHT)-type heating and subsequent long-term storage. Pan-frying, however, induced phytosterol oxidation and was classified as a rather deteriorative process. Overall, the findings indicated that although phytosterols and stanols are stable in normal food processing conditions, attention should be paid to their use in frying. Complex interactions between other food constituents also suggested that when new phytosterol-enriched foods are developed their oxidative stability must first be established. The results presented here will assist in choosing safe conditions for phytosterol/stanol enrichment.

Dynamic nature of proteins - interpretation of residual dipolar couplings

Protein conformations and dynamics can be studied by nuclear magnetic resonance spectroscopy using dilute liquid crystalline samples. This work clarifies the interpretation of residual dipolar coupling data yielded by the experiments. It was discovered that unfolded proteins without any additional structure beyond that of a mere polypeptide chain exhibit residual dipolar couplings. Also, it was found that molecular dynamics induce fluctuations in the molecular alignment and doing so affect residual dipolar couplings. The finding clarified the origins of low order parameter values observed earlier. The work required the development of new analytical and computational methods for the prediction of intrinsic residual dipolar coupling profiles for unfolded proteins. The presented characteristic chain model is able to reproduce the general trend of experimental residual dipolar couplings for denatured proteins. The details of experimental residual dipolar coupling profiles are beyond the analytical model, but improvements are proposed to achieve greater accuracy. A computational method for rapid prediction of unfolded protein residual dipolar couplings was also developed. Protein dynamics were shown to modulate the effective molecular alignment in a dilute liquid crystalline medium. The effects were investigated from experimental and molecular dynamics generated conformational ensembles of folded proteins. It was noted that dynamics induced alignment is significant especially for the interpretation of molecular dynamics in small, globular proteins. A method of correction was presented. Residual dipolar couplings offer an attractive possibility for the direct observation of protein conformational preferences and dynamics. The presented models and methods of analysis provide significant advances in the interpretation of residual dipolar coupling data from proteins.

Molecular dynamics studies of nanoparticle impacts

This thesis concerns the dynamics of nanoparticle impacts on solid surfaces. These impacts occur, for instance, in space, where micro- and nanometeoroids hit surfaces of planets, moons, and spacecraft. On Earth, materials are bombarded with nanoparticles in cluster ion beam devices, in order to clean or smooth their surfaces, or to analyse their elemental composition. In both cases, the result depends on the combined effects of countless single impacts. However, the dynamics of single impacts must be understood before the overall effects of nanoparticle radiation can be modelled. In addition to applications, nanoparticle impacts are also important to basic research in the nanoscience field, because the impacts provide an excellent case to test the applicability of atomic-level interaction models to very dynamic conditions. In this thesis, the stopping of nanoparticles in matter is explored using classical molecular dynamics computer simulations. The materials investigated are gold, silicon, and silica. Impacts on silicon through a native oxide layer and formation of complex craters are also simulated. Nanoparticles up to a diameter of 20 nm (315000 atoms) were used as projectiles. The molecular dynamics method and interatomic potentials for silicon and gold are examined in this thesis. It is shown that the displacement cascade expansionmechanism and crater crown formation are very sensitive to the choice of atomic interaction model. However, the best of the current interatomic models can be utilized in nanoparticle impact simulation, if caution is exercised. The stopping of monatomic ions in matter is understood very well nowadays. However, interactions become very complex when several atoms impact on a surface simultaneously and within a short distance, as happens in a nanoparticle impact. A high energy density is deposited in a relatively small volume, which induces ejection of material and formation of a crater. Very high yields of excavated material are observed experimentally. In addition, the yields scale nonlinearly with the cluster size and impact energy at small cluster sizes, whereas in macroscopic hypervelocity impacts, the scaling 2 is linear. The aim of this thesis is to explore the atomistic mechanisms behind the nonlinear scaling at small cluster sizes. It is shown here that the nonlinear scaling of ejected material yield disappears at large impactor sizes because the stopping mechanism of nanoparticles gradually changes to the same mechanism as in macroscopic hypervelocity impacts. The high yields at small impactor size are due to the early escape of energetic atoms from the hot region. In addition, the sputtering yield is shown to depend very much on the spatial initial energy and momentum distributions that the nanoparticle induces in the material in the first phase of the impact. At the later phases, the ejection of material occurs by several mechanisms. The most important mechanism at high energies or at large cluster sizes is atomic cluster ejection from the transient liquid crown that surrounds the crater. The cluster impact dynamics detected in the simulations are in agreement with several recent experimental results. In addition, it is shown that relatively weak impacts can induce modifications on the surface of an amorphous target over a larger area than was previously expected. This is a probable explanation for the formation of the complex crater shapes observed on these surfaces with atomic force microscopy. Clusters that consist of hundreds of thousands of atoms induce long-range modifications in crystalline gold.

Studies on Binary Time Series Models with Applications to Empirical Macroeconomics and Finance

This thesis studies binary time series models and their applications in empirical macroeconomics and finance. In addition to previously suggested models, new dynamic extensions are proposed to the static probit model commonly used in the previous literature. In particular, we are interested in probit models with an autoregressive model structure. In Chapter 2, the main objective is to compare the predictive performance of the static and dynamic probit models in forecasting the U.S. and German business cycle recession periods. Financial variables, such as interest rates and stock market returns, are used as predictive variables. The empirical results suggest that the recession periods are predictable and dynamic probit models, especially models with the autoregressive structure, outperform the static model. Chapter 3 proposes a Lagrange Multiplier (LM) test for the usefulness of the autoregressive structure of the probit model. The finite sample properties of the LM test are considered with simulation experiments. Results indicate that the two alternative LM test statistics have reasonable size and power in large samples. In small samples, a parametric bootstrap method is suggested to obtain approximately correct size. In Chapter 4, the predictive power of dynamic probit models in predicting the direction of stock market returns are examined. The novel idea is to use recession forecast (see Chapter 2) as a predictor of the stock return sign. The evidence suggests that the signs of the U.S. excess stock returns over the risk-free return are predictable both in and out of sample. The new "error correction" probit model yields the best forecasts and it also outperforms other predictive models, such as ARMAX models, in terms of statistical and economic goodness-of-fit measures. Chapter 5 generalizes the analysis of univariate models considered in Chapters 2 4 to the case of a bivariate model. A new bivariate autoregressive probit model is applied to predict the current state of the U.S. business cycle and growth rate cycle periods. Evidence of predictability of both cycle indicators is obtained and the bivariate model is found to outperform the univariate models in terms of predictive power.

Nonlinear mixture autoregressive model: economic applications

The aim of this dissertation is to model economic variables by a mixture autoregressive (MAR) model. The MAR model is a generalization of linear autoregressive (AR) model. The MAR -model consists of K linear autoregressive components. At any given point of time one of these autoregressive components is randomly selected to generate a new observation for the time series. The mixture probability can be constant over time or a direct function of a some observable variable. Many economic time series contain properties which cannot be described by linear and stationary time series models. A nonlinear autoregressive model such as MAR model can a plausible alternative in the case of these time series. In this dissertation the MAR model is used to model stock market bubbles and a relationship between inflation and the interest rate. In the case of the inflation rate we arrived at the MAR model where inflation process is less mean reverting in the case of high inflation than in the case of normal inflation. The interest rate move one-for-one with expected inflation. We use the data from the Livingston survey as a proxy for inflation expectations. We have found that survey inflation expectations are not perfectly rational. According to our results information stickiness play an important role in the expectation formation. We also found that survey participants have a tendency to underestimate inflation. A MAR model has also used to model stock market bubbles and crashes. This model has two regimes: the bubble regime and the error correction regime. In the error correction regime price depends on a fundamental factor, the price-dividend ratio, and in the bubble regime, price is independent of fundamentals. In this model a stock market crash is usually caused by a regime switch from a bubble regime to an error-correction regime. According to our empirical results bubbles are related to a low inflation. Our model also imply that bubbles have influences investment return distribution in both short and long run.

Analysis of forest soil chemistry and hydrology with a dynamic model ACIDIC.

In this study we analyze how the ion concentrations in forest soil solution are determined by hydrological and biogeochemical processes. A dynamic model ACIDIC was developed, including processes common to dynamic soil acidification models. The model treats up to eight interacting layers and simulates soil hydrology, transpiration, root water and nutrient uptake, cation exchange, dissolution and reactions of Al hydroxides in solution, and the formation of carbonic acid and its dissociation products. It includes also a possibility to a simultaneous use of preferential and matrix flow paths, enabling the throughfall water to enter the deeper soil layers in macropores without first reacting with the upper layers. Three different combinations of routing the throughfall water via macro- and micropores through the soil profile is presented. The large vertical gradient in the observed total charge was simulated succesfully. According to the simulations, gradient is mostly caused by differences in the intensity of water uptake, sulfate adsorption and organic anion retention at the various depths. The temporal variations in Ca and Mg concentrations were simulated fairly well in all soil layers. For H+, Al and K there were much more variation in the observed than in the simulated concentrations. Flow in macropores is a possible explanation for the apparent disequilibrium of the cation exchange for H+ and K, as the solution H+ and K concentrations have great vertical gradients in soil. The amount of exchangeable H+ increased in the O and E horizons and decreased in the Bs1 and Bs2 horizons, the net change in whole soil profile being a decrease. A large part of the decrease of the exchangeable H+ in the illuvial B horizon was caused by sulfate adsorption. The model produces soil water amounts and solution ion concentrations which are comparable to the measured values, and it can be used in both hydrological and chemical studies of soils.