High Dimensional Time Series — New Techniques and Applications

The past decade witnessed the rapid development of high dimensional statistics in deterministic design. High dimensional time series analysis, due to the time dependency, still faces several theoretical challenges. Among the time series models, the Vector Error Correction Model (VECM) is especially complicated because of the non-stationary components. The classical estimation strategies (e.g. Johansen\u27s approach) fail to provide consistent estimates for dimensions larger than three. Moreover, it is impossible to apply existing statistical methods to determine VECM in high dimensions, i.e. when the dimension is allowed to increase with the number of observations or even larger than that. This dissertation aims at providing feasible regularized methods, which can determine and estimate high dimensional VECM with robust statistical properties. The detailed analysis is divided into three parts. First I develop new tailored Lasso-type methods to estimate VECM and prove their statistical properties, in a setting where the cointegration rank is fixed but unknown and the dimension is large but not increasing with sample size. Then this methodology is extended to cover also the high dimensional case with moving rank and dimension. For this the estimation strategy must be changed and the statistical analysis requires completely different high-dimensional techniques. Under specific assumptions, I propose the estimation strategy in the ultra-high dimensional case. From the application side, these techniques are highly valuable for appropriately treating complex potentially non-stationary systems not only in economics and finance but also in weather and climate systems. I also illustrate this for a portfolio of Credit Default Swaps in a banking-sovereign network and identify different risk clusters by measuring the interconnectedness over time, which is beyond the scope of previous methodologies. Moreover, I provide a detailed empirical study on a high-frequency portfolio where new high-dimensional time series techniques allow to account for liquidity effects through the Limit Order Book in a very detailed way. With this the new spillover channels in the system can be identified

Group-Lasso on Splines for Spectrum Cartography

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finitely-parameterized (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that ``better'' explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Simulated tests corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced.Comment: Submitted to IEEE Transactions on Signal Processin

Methodologies for Future Vehicular Digital Twins

The role of wireless communications in various domains of intelligent transportation systems is significant; it is evident that dependable message exchange between nodes (cars, bikes, pedestrians, infrastructure, etc.) has to be guaranteed to fulfill the stringent requirements for future transportation systems. A precise site-specific digital twin is seen as a key enabler for the cost-effective development and validation of future vehicular communication systems. Furthermore, achieving a realistic digital twin for dependable wireless communications requires accurate measurement, modeling, and emulation of wireless communication channels. However, contemporary approaches in these domains are not efficient enough to satisfy the foreseen needs. In this position paper, we overview the current solutions, indicate their limitations, and discuss the most prospective paths for future investigation.Comment: Submitted to IEEE Intelligent Transportation Systems Magazin

Angular dispersion of radio waves in mobile channels

Multi-antenna techniques are an important solution for significantly increasing the bandwidth efficiency of mobile wireless data transmission systems. Effective and reliable design of these multi-antenna systems requires thorough knowledge of radiowave propagation in the urban environment. The aim of the work presented in this thesis is to obtain a better physical understanding of radiowave propagation in mobile radio channels in order to provide a basis for the improvement of radiowave propagation prediction techniques for urban environments using knowledge from 3-D propagation experiments and simulations combined with space-wave modelling. In particular, the work focusses on: the development of an advanced 3-D mobile channel sounding system, obtaining propagation measurement data from mobile radio propagation experiments, the analysis of measured data and the modelling of angular dispersive scattering effects for the improvement of deterministic propagation prediction models. The first part of the study presents the design, implementation and verification of a wideband high-resolution measurement system for the characterisation of angular dispersion in mobile channels. The system uses complex impulse response data obtained from a novel 3-D tilted-cross switched antenna array as input to an improved version of 3-D Unitary ESPRIT. It is capable of characterising the delay and angular properties of physically-nonstationary radio channels at moderate urban speeds with high resolution in both azimuth and elevation. For the first time, omnidirectional video data that were captured during the measurements are used in combination with the measurement results to accurately identify and relate the received radio waves directly to the actual environment while moving through it. The second part of the study presents the results of experiments in which the highresolution measurement system, described in the first part, is used in several mobile outdoor experiments in different scenarios. The objective of these measurements was to gain more knowledge in order to improve the understanding of radiowave propagation. From these results the dispersive effects in the angular domain, caused by rough building surfaces and other irregular structures was paid particular attention. These effects not only influence the total amount of received power in dense urban environments, but can also have a large impact on the performance and deployment of multi-antenna systems. To improve the data representation and support further data analysis a hierarchical clustering method is presented that can successfully identify clusters of multipath signal components in multidimensional data. By using the data obtained from an omnidirectional video camera the clusters can be related directly to the environment and the scattering effects of specific objects can be isolated. These results are important in order to improve and calibrate deterministic propagation models. In the third part of the study a new method is presented to account for the angular dispersion caused by irregular surfaces in ray-tracing based propagation prediction models. The method is based on assigning an effective roughness to specific surfaces. Unlike the conventional reflection reduction factor for Gaussian surfaces, that only reduces the ray power, the new method also distributes power in the angular domain. The results of clustered measurement data are used to calibrated the model and show that this leads to improved channel representations that are better matched to the real-world channel behavior

Estimation and tracking of rapidly time-varying broadband acoustic communication channels

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2006This thesis develops methods for estimating wideband shallow-water acoustic communication channels. The very shallow water wideband channel has three distinct features: large dimension caused by extensive delay spread; limited number of degrees of freedom (DOF) due to resolvable paths and inter-path correlations; and rapid fluctuations induced by scattering from the moving sea surface. Traditional LS estimation techniques often fail to reconcile the rapid fluctuations with the large dimensionality. Subspace based approaches with DOF reduction are confronted with unstable subspace structure subject to significant changes over a short period of time. Based on state-space channel modeling, the first part of this thesis develops algorithms that jointly estimate the channel as well as its dynamics. Algorithms based on the Extended Kalman Filter (EKF) and the Expectation Maximization (EM) approach respectively are developed. Analysis shows conceptual parallels, including an identical second-order innovation form shared by the EKF modification and the suboptimal EM, and the shared issue of parameter identifiability due to channel structure, reflected as parameter unobservability in EKF and insufficient excitation in EM. Modifications of both algorithms, including a two-model based EKF and a subspace EM algorithm which selectively track dominant taps and reduce prediction error, are proposed to overcome the identifiability issue. The second part of the thesis develops algorithms that explicitly find the sparse estimate of the delay-Doppler spread function. The study contributes to a better understanding of the channel physical constraints on algorithm design and potential performance improvement. It may also be generalized to other applications where dimensionality and variability collide.Financial support for this thesis research was provided by the Office of Naval Research and the WHOI Academic Program Office

Time- and Frequency-Varying KK-Factor of Non-Stationary Vehicular Channels for Safety Relevant Scenarios

Vehicular communication channels are characterized by a non-stationary time- and frequency-selective fading process due to fast changes in the environment. We characterize the distribution of the envelope of the first delay bin in vehicle-to-vehicle channels by means of its Rician $K$-factor. We analyze the time-frequency variability of this channel parameter using vehicular channel measurements at 5.6 GHz with a bandwidth of 240 MHz for safety-relevant scenarios in intelligent transportation systems (ITS). This data enables a frequency-variability analysis from an IEEE 802.11p system point of view, which uses 10 MHz channels. We show that the small-scale fading of the envelope of the first delay bin is Ricean distributed with a varying $K$-factor. The later delay bins are Rayleigh distributed. We demonstrate that the $K$-factor cannot be assumed to be constant in time and frequency. The causes of these variations are the frequency-varying antenna radiation patterns as well as the time-varying number of active scatterers, and the effects of vegetation. We also present a simple but accurate bi-modal Gaussian mixture model, that allows to capture the $K$-factor variability in time for safety-relevant ITS scenarios.Comment: 26 pages, 12 figures, submitted to IEEE Transactions on Intelligent Transportation Systems for possible publicatio

Detection of non-stationary dynamics using sub-space based representations, cyclic based and variability constraints

La siguiente Tesis de Maestría propone una metodología para el análisis de series de tiempo no-estacionarias con el propósito de filtrado y detección de ruido en reconocimiento de patrones. La metodología se encuentra dividida en dos etapas: el análisis de comportamientos no-estacionarios que recaen en procesos cíclicos y como diferentes componentes no-periódicos afectan el análisis de la señal. El segundo enfoque, está centrado en el problema de extracción de series de tiempo no-estacionarias que afectan procesos estacionarios. Ambos esquemas están basados en restricciones de (ciclo-)estacionariead y representaciones basadas en subespacios de manera que mediante la evaluación de las dinámicas de la señal sea posible identificar las componentes no-estacionarias indeseadas. Los resultados se muestran para cada enfoque de manera independiente por medio de datos sintéticos y reales, el desempeño obtenido muestra una gran capacidad de detección, rechazo y/o extracción de ruido y artefactos en series de tiempo (ciclo-)estacionarias usando restricciones de estacionariedad así como condiciones cíclicas basadas en la naturaleza de la señalAbstract : The present Master’s Thesis proposes a methodology for the non–stationary time-series analysis for filtering and noise rejection purposes in pattern recognition. The methodology is divided into two different approaches: the analysis of periodic non–stationary behavior that relies into a cyclic process and how additional non–cyclic non–stationarities disrupt and affect the signal processing. Second approach deals with the problem of non–stationary signal extraction that affects inherent weak stationary processes. Both frameworks of analysis take base on (cyclo-)stationary constraints and subspace based representations in order to assess and characterize the signals dynamics to facilitate the identification of the undesired non–stationary components. Results are shown over each approach with different real and synthetic data, the obtained performances show high rejection, detection and extraction capabilities for noise and artifacts in (cyclo)–stationary signals using external and internal based constraints of analysis and high separation capability for stationary signalsMaestrí