The analysis of experimental data that have been observed at different points in time leads to new and unique problems in statistical modeling and inference. The obvious correlation introduced by the sampling of adjacent points in time can severely restrict the applicability of the many conventional statistical methods traditionally dependent on the assumption that these adjacent observations are independent andidentically distributed. The systematic approach by which one goes about answering the mathematical and statistical questions posed by these time correlations is commonly referred to as time series analysis (TSA).Time series modeling (TSM) plays a key role in a wide range of real-life problems that have a temporal component. Modern time series problems often pose significant challenges for the existing techniques both in terms of their complexity, structure and size. While traditional methods have focused on parametric models informed by domain expertise, modern machine learning (ML) methods provide a means to learn temporal dynamics in a purely data-driven manner. With the increasing data availability and computing power in recent times, machine learning has become a vital part of the next generation of time series models. Thus, there is both a great need and an exciting opportunity for the machine learning community to develop theory, models and algorithms specifically for the purpose of processing and analyzing time series data.The impact of time series modelling and analysis on scientific applications can be partially documented by analysing problems of various diverse fields in which important time series problems may arise. Modern time series problems are characterized by complexity. Also, since real-world systems often evolve under transient conditions, the signals/time series tend to exhibit various forms of non-stationarity. As far as mathematical models are concerned, they can be categorized in many different ways. They can be linear or non-linear, static or dynamic, continuous distinct in time, deterministic or contemplative. The proper model selection to accurately describe a system depends on the system under study, on whether the operation of the system is a-priory known or not, as well as on the purpose of the implementation. This dissertation presents developments in nonlinear and non-static time series models under a machine learning framework, comparing their performance in real-life application scenarios related to geoinformatics as well as environmental applications.In this dissertation is provided a comparative analysis that evaluates the performance of several deep learning (DL) architectures on a large number of time series datasets of different nature and for different applications. Two main fruitful research fields are discussed here which were strategically chosen in order to address current cross-disciplinary research priorities attracting the interest of geoinformatics communities. The first problem is related to ionospheric Total Electron Content (TEC) modeling which is an important issue in many real-time Global Navigation System Satellites (GNSS) applications. Reliable and fast knowledge about ionospheric variations becomes increasingly important. GNSS users of single-frequency receivers and satellite navigation systems need accurate corrections to remove signal degradation effects caused by the ionosphere. Ionospheric modeling using signal-processing techniques is the subject of discussion in the present contribution. The next problem under discussion is energy disaggregation which is an important issue for energy efficiency and energy consumption awareness. Reliable and fast knowledge about residential energy consumption at appliance level becomes increasingly important nowadays and it is an important mitigation measure to prevent energy wastage. Energy disaggregation or Non-intrusive load monitoring (NILM) is a single channel blind source separation problem where the task is to estimate the consumption of each electrical appliance given the total energy consumption. For both problems various deep learning models (DL) are proposed that cover various aspects of the problem under study, whereas experimental results indicate the proposed methods' superiority compared to the current state of the art.
A Class of Copula-Based Bivariate Poisson Time Series Models with Applications
