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.

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.

Valuation of reduced eutrophication in the Gulf of Finland : Choice experiment with attention to heterogeneous and discontinuous preferences and respondent uncertainty

Eutrophication of the Baltic Sea is a serious problem. This thesis estimates the benefit to Finns from reduced eutrophication in the Gulf of Finland, the most eutrophied part of the Baltic Sea, by applying the choice experiment method, which belongs to the family of stated preference methods. Because stated preference methods have been subject to criticism, e.g., due to their hypothetical survey context, this thesis contributes to the discussion by studying two anomalies that may lead to biased welfare estimates: respondent uncertainty and preference discontinuity. The former refers to the difficulty of stating one s preferences for an environmental good in a hypothetical context. The latter implies a departure from the continuity assumption of conventional consumer theory, which forms the basis for the method and the analysis. In the three essays of the thesis, discrete choice data are analyzed with the multinomial logit and mixed logit models. On average, Finns are willing to contribute to the water quality improvement. The probability for willingness increases with residential or recreational contact with the gulf, higher than average income, younger than average age, and the absence of dependent children in the household. On average, for Finns the relatively most important characteristic of water quality is water clarity followed by the desire for fewer occurrences of blue-green algae. For future nutrient reduction scenarios, the annual mean household willingness to pay estimates range from 271 to 448 and the aggregate welfare estimates for Finns range from 28 billion to 54 billion euros, depending on the model and the intensity of the reduction. Out of the respondents (N=726), 72.1% state in a follow-up question that they are either Certain or Quite certain about their answer when choosing the preferred alternative in the experiment. Based on the analysis of other follow-up questions and another sample (N=307), 10.4% of the respondents are identified as potentially having discontinuous preferences. In relation to both anomalies, the respondent- and questionnaire-specific variables are found among the underlying causes and a departure from standard analysis may improve the model fit and the efficiency of estimates, depending on the chosen modeling approach. The introduction of uncertainty about the future state of the Gulf increases the acceptance of the valuation scenario which may indicate an increased credibility of a proposed scenario. In conclusion, modeling preference heterogeneity is an essential part of the analysis of discrete choice data. The results regarding uncertainty in stating one s preferences and non-standard choice behavior are promising: accounting for these anomalies in the analysis may improve the precision of the estimates of benefit from reduced eutrophication in the Gulf of Finland.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Land leasing, land degradation and agricultural productivity in Finland

This study analysed whether the land tenure insecurity problem has led to a decline in long-term land improvements (liming and phosphorus fertilization) under the Common Agricultural Policy (CAP) and Nordic production conditions in European Union (EU) countries such as Finland. The results suggests that under traditional cash lease contracts, which are encouraged by the existing land leasing regulations and agricultural subsidy programs, the land tenure insecurity problem on leased land reduces land improvements that have a long pay-back period. In particular, soil pH was found to be significantly lower on land cultivated under a lease contract compared to land owned by the farmers themselves. The results also indicate that land improvements could not be reversed by land markets, because land owners would otherwise have carried out land improvements even if not farming by themselves. To reveal the causality between land tenure and land improvements, the dynamic optimisation problem was solved by a stochastic dynamic programming routine with known parameters for one-period returns and transition equations. The model parameters represented Finnish soil quality and production conditions. The decision rules were solved for alternative likelihood scenarios over the continuation of the fixed-term lease contract. The results suggest that as the probability of non-renewal of the lease contract increases, farmers quickly reduce investments in irreversible land improvements and, thereafter, yields gradually decline. The simulations highlighted the observed trends of a decline in land improvements on land parcels that are cultivated under lease contracts. Land tenure has resulted in the neglect of land improvement in Finland. This study aimed to analyze whether these challenges could be resolved by a tax policy that encourages land sales. Using Finnish data, real estate tax and a temporal relaxation on the taxation of capital gains showed some potential for the restructuring of land ownership. Potential sellers who could not be revealed by traditional logit models were identified with the latent class approach. Those landowners with an intention to sell even without a policy change were sensitive to temporal relaxation in the taxation of capital gains. In the long term, productivity and especially productivity growth are necessary conditions for the survival of farms and the food industry in Finland. Technical progress was found to drive the increase in productivity. The scale had only a moderate effect and for the whole study period (1976–2006) the effect was close to zero. Total factor productivity (TFP) increased, depending on the model, by 0.6–1.7% per year. The results demonstrated that the increase in productivity was hindered by the policy changes introduced in 1995. It is also evidenced that the increase in land leasing is connected to these policy changes. Land institutions and land tenure questions are essential in agricultural and rural policies on all levels, from local to international. Land ownership and land titles are commonly tied to fundamental political, economic and social questions. A fair resolution calls for innovative and new solutions both on national and international levels. However, this seems to be a problem when considering the application of EU regulations to member states inheriting divergent landownership structures and farming cultures. The contribution of this study is in describing the consequences of fitting EU agricultural policy to Finnish agricultural land tenure conditions and heritage.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Rolling tachyons, random matrices, and Coulomb gas thermodynamics

Time-dependent backgrounds in string theory provide a natural testing ground for physics concerning dynamical phenomena which cannot be reliably addressed in usual quantum field theories and cosmology. A good, tractable example to study is the rolling tachyon background, which describes the decay of an unstable brane in bosonic and supersymmetric Type II string theories. In this thesis I use boundary conformal field theory along with random matrix theory and Coulomb gas thermodynamics techniques to study open and closed string scattering amplitudes off the decaying brane. The calculation of the simplest example, the tree-level amplitude of n open strings, would give us the emission rate of the open strings. However, even this has been unknown. I will organize the open string scattering computations in a more coherent manner and will argue how to make further progress.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Key Factors Influencing Economic Relationships and Communication in Finnish Food Chains

The aim of this report is to discuss the role of the relationship type and communication in two Finnish food chains, namely the pig meat-to-sausage (pig meat chain) and the cereal-to-rye bread (rye chain) chains. Furthermore, the objective is to examine those factors influencing the choice of a relationship type and the sustainability of a business relationship. Altogether 1808 questionnaires were sent to producers, processors and retailers operating in these two chains of which 224 usable questionnaires were returned (the response rate being 12.4%). The great majority of the respondents (98.7%) were small businesses employing less than 50 people. Almost 70 per cent of the respondents were farmers. In both chains, formal contracts were stated to be the most important relationship type used with business partners. Although for many businesses written contracts are a common business practice, the essential role of the contracts was the security they provide regarding the demand/supply and quality issues. Relative to the choice of the relationship types, the main difference between the two chains emerged especially with the prevalence of spot markets and financial participation arrangements. The usage of spot markets was significantly more common in the rye chain when compared to the pig meat chain, while, on the other hand, financial participation arrangements were much more common among the businesses in the pig meat chain than in the rye chain. Furthermore, the analysis showed that most of the businesses in the pig meat chain claimed not to be free to choose the relationship type they use. Especially membership in a co-operative and practices of a business partner were mentioned as the reasons limiting this freedom of choice. The main business relations in both chains were described as having a long-term orientation and being based on formal written contracts. Typical for the main business relationships was also that they are not based on the existence of the key persons only; the relationship would remain even if the key people left the business. The quality of these relationships was satisfactory in both chains and across all the stakeholder groups, though the downstream processors and the retailers had a slightly more positive view on their main business partners than the farmers and the upstream processors. The businesses operating in the pig meat chain seemed also to be more dependent on their main business relations when compared to the businesses in the rye chain. Although the communication means were rather similar in both chains (the phone being the most important), there was some variation between the chains concerning the communication frequency necessary to maintain the relationship with the main business partner. In short, the businesses in the pig meat chain seemed to appreciate more frequent communication with their main business partners when compared to the businesses in the rye chain. Personal meetings with the main business partners were quite rare in both chains. All the respondent groups were, however, fairly satisfied with the communication frequency and information quality between them and the main business partner. The business cultures could be argued to be rather hegemonic among the businesses both in the pig meat and rye chains. Avoidance of uncertainty, appreciation of long-term orientation and independence were considered important factors in the business cultures. Furthermore, trust, commitment and satisfaction in business partners were thought to be essential elements of business operations in all the respondent groups. In order to investigate which factors have an effect on the choice of a relationship type, several hypotheses were tested by using binary and multinomial logit analyses. According to these analyses it could be argued that avoidance of uncertainty and risk has a certain effect on the relationship type chosen, i.e. the willingness to avoid uncertainty increases the probability to choose stable relationships, like repeated market transactions and formal written contracts, but not necessary those, which require high financial commitment (like financial participation arrangements). The probability of engaging in financial participation arrangements seemed to increase with long-term orientation. The hypotheses concerning the sustainability of the economic relations were tested by using structural equation model (SEM). In the model, five variables were found to have a positive and statistically significant impact on the sustainable economic relationship construct. Ordered relative to their importance, those factors are: (i) communication quality, (ii) personal bonds, (iii) equal power distribution, (iv) local embeddedness and (v) competition.

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.

Topics in Spatial Econometrics - With Applications to House Prices

Topics in Spatial Econometrics — With Applications to House Prices Spatial effects in data occur when geographical closeness of observations influences the relation between the observations. When two points on a map are close to each other, the observed values on a variable at those points tend to be similar. The further away the two points are from each other, the less similar the observed values tend to be. Recent technical developments, geographical information systems (GIS) and global positioning systems (GPS) have brought about a renewed interest in spatial matters. For instance, it is possible to observe the exact location of an observation and combine it with other characteristics. Spatial econometrics integrates spatial aspects into econometric models and analysis. The thesis concentrates mainly on methodological issues, but the findings are illustrated by empirical studies on house price data. The thesis consists of an introductory chapter and four essays. The introductory chapter presents an overview of topics and problems in spatial econometrics. It discusses spatial effects, spatial weights matrices, especially k-nearest neighbours weights matrices, and various spatial econometric models, as well as estimation methods and inference. Further, the problem of omitted variables, a few computational and empirical aspects, the bootstrap procedure and the spatial J-test are presented. In addition, a discussion on hedonic house price models is included. In the first essay a comparison is made between spatial econometrics and time series analysis. By restricting the attention to unilateral spatial autoregressive processes, it is shown that a unilateral spatial autoregression, which enjoys similar properties as an autoregression with time series, can be defined. By an empirical study on house price data the second essay shows that it is possible to form coordinate-based, spatially autoregressive variables, which are at least to some extent able to replace the spatial structure in a spatial econometric model. In the third essay a strategy for specifying a k-nearest neighbours weights matrix by applying the spatial J-test is suggested, studied and demonstrated. In the final fourth essay the properties of the asymptotic spatial J-test are further examined. A simulation study shows that the spatial J-test can be used for distinguishing between general spatial models with different k-nearest neighbours weights matrices. A bootstrap spatial J-test is suggested to correct the size of the asymptotic test in small samples.

Using a botanic garden collection to test a bioclimatic vegetation scheme

Vegetation maps and bioclimatic zone classifications communicate the vegetation of an area and are used to explain how the environment regulates the occurrence of plants on large scales. Many practises and methods for dividing the world’s vegetation into smaller entities have been presented. Climatic parameters, floristic characteristics, or edaphic features have been relied upon as decisive factors, and plant species have been used as indicators for vegetation types or zones. Systems depicting vegetation patterns that mainly reflect climatic variation are termed ‘bioclimatic’ vegetation maps. Based on these it has been judged logical to deduce that plants moved between corresponding bioclimatic areas should thrive in the target location, whereas plants moved from a different zone should languish. This principle is routinely applied in forestry and horticulture but actual tests of the validity of bioclimatic maps in this sense seem scanty. In this study I tested the Finnish bioclimatic vegetation zone system (BZS). Relying on the plant collection of Helsinki University Botanic Garden’s Kumpula collection, which according to the BZS is situated at the northern limit of the hemiboreal zone, I aimed to test how the plants’ survival depends on their provenance. My expectation was that plants from the hemiboreal or southern boreal zones should do best in Kumpula, whereas plants from more southern and more northern zones should show progressively lower survival probabilities. I estimated probability of survival using collection database information of plant accessions of known wild origin grown in Kumpula since the mid 1990s, and logistic regression models. The total number of accessions I included in the analyses was 494. Because of problems with some accessions I chose to separately analyse a subset of the complete data, which included 379 accessions. I also analysed different growth forms separately in order to identify differences in probability of survival due to different life strategies. In most analyses accessions of temperate and hemiarctic origin showed lower survival probability than those originating from any of the boreal subzones, which among them exhibited rather evenly high probabilities. Exceptionally mild and wet winters during the study period may have killed off hemiarctic plants. Some winters may have been too harsh for temperate accessions. Trees behaved differently: they showed an almost steadily increasing survival probability from temperate to northern boreal origins. Various factors that could not be controlled for may have affected the results, some of which were difficult to interpret. This was the case in particular with herbs, for which the reliability of the analysis suffered because of difficulties in managing their curatorial data. In all, the results gave some support to the BZS, and especially its hierarchical zonation. However, I question the validity of the formulation of the hypothesis I tested since it may not be entirely justified by the BZS, which was designed for intercontinental comparison of vegetation zones, but not specifically for transcontinental provenance trials. I conclude that botanic gardens should pay due attention to information management and curational practices to ensure the widest possible applicability of their plant collections.