Random Models in Time and Space with Financial, Economics and Engineering Applications : Structural Covariance in Space and Stochastic Variability in Time

Sammanfattning: In this thesis, we model stochastic processes in time and space. We focus on the processes whose covariance structure is either changing over the time span, or depends on the location in space. We develop models that appropriately describe and analyze such data behaviors in various different fields including finance, economics and engineering. This thesis begins with an introductory section which provides an overview of the topic before delving into the details of five papers (I–V).In paper I, we explore the multivariate spatial regression model, commonly used in spatial econometrics. We develop a new and extended version of this model, with the capacity to explicitly account for the intralocation feedback effects between the variables; the standard models fail to account for this factor properly leading to misrepresentation of the interlocation parameters in these models. We provide statistical inferences and suggest various estimation methods, and we also extend the model further to allow for more flexibility.In paper II, we then utilize the developed intralocation feedback effects model to simultaneously account for both inter- and intralocation effects among different financial variables. In particular, we employ such a model to investigate the comovements among international stock and bond markets, where we use geographical neighborhood and bilateral trade to define countries’ proximity. Our aim is to find if there exist meaningful and significant within- and cross-country dependences between stock and bond returns.In paper III, we propose a simply structured model featuring generalized asymmetric Laplace distribution as its marginal capable of capturing a certain behavior frequently observed in engineering, biometric and financial data. This behavior leads to non-Gaussian features in stochastic data in the long run, while the data appear to remain within the Gaussian framework in the short run. Such non-Gaussian features are usually attributed to considerable modulation in the data variation in long run. The proposed model is obtained from an autoregressive-type stationary process with gamma distributed marginal as variance–mean mixture scaling of a stationary Gaussian process.In paper IV, we then use a version of the above-mentioned autoregressive gamma variance model for an engineering application, modeling the topography of road profiles. The model encompasses variability exhibited by a Gaussian autoregressive process with randomly varying variance. We propose various innovative estimation methods to fit the parameters of these merged processes separately. We demonstrate that the model is able to accurately represent hilliness features of road topography providing a significant improvement over a purely Gaussian model with an intuitive interpretation for the parameters. The model is helping to improve utility-vehicle design by incorporating a more precise road description into the simulation step.In paper V, we deal with the autocorrelated data whose variance varies over time due to contamination by the outlying processes. The presence of outlying processes leads to non-Gaussianity in the data distribution. Dealing with such a situation is of special importance for the data monitoring in statistical process (quality) control. In this paper, we present a novel design for a robust quality control chart suitable for time series observations. Our chart is robust against the effects of random outlying processes or, equivalently, robust against a broad range of random variation in the process variance.