Detecting patterns in Time Series Data with applications in Official Statistics

This thesis examines the issue of detecting components or features within time series data in automatic procedures. We begin by introducing the concept of Wavelets and briefly show their usage as a tool for detection. This leads to our first contribution which is a novel method using wavelets for identifying correlation structures in time series data which are often ambiguous with very different contexts. Using the properties of the wavelet transform we show the ability to distinguish between short memory models with changepoints and long memory models. The next two Chapters consider seasonality within data, which is often present in time series used in Offical Statistics. We first describe the historical evolution of identification of seasonality, comparing and contrasting methodology as it has expanded throughout time. Following this, motivated by the increased use of high-frequency time series in Official Statistics and a lack of methods for identifying low-frequency seasonal components within high-frequency data, we present a method for identifying periodicity in a series with the use of a simple wavelet decomposition. Presented with theoretical results and simulations, we show how the seasonality of a series is uniquely represented within a wavelet transform and use this to identify low frequency components which are often overlooked in favour of a trend, with very different interpretations. Finally, beginning with the motivation of forecasting European Area GDP at the current time point, we show the effectiveness of an algorithm which detects the most useful data and structures for a Dynamic Factor Model. We show its effectiveness in reducing forecasting errors but show that under large scale simulation that the recovery of the true structure over two dimensions is a difficult task. All the chapters of this thesis are motivated by, and give applications to, time series from different areas of Official Statistics

Change point analysis in a state space framework to monthly temperature data in European cities

In this work, we present time series of monthly average temperatures in several Euro- pean locations which were statistically analyzed using a state space approach, where it is considered a model with a deterministic seasonal component and a stochastic trend. The analysis of smoother prediction of the stochastic trend and its comparison in a tem- poral viewpoint can reveal patterns about warming in Europe. The temperature rise rates in Europe seem to have increased in the last decades when compared with longer periods, hence a change point detection method is applied to the trend component in order to identify these possible changes in the monthly temperature rise rates. The adopted methodology pointed out, for most series a change point in the late eighties.publishe

Statistical Modelling of Water Quality Time Series – The River Vouga Basin Case Study

The focus of this work is on contributions to the analysis of time series of water quality variables. The study of these time series has characteristics related to data collection procedures, as well as to several economic and geographic aspects. Some characteristics of water quality variables pose challenges to their statistical modelling, namely, seasonality, change-point detection, the existence of outliers, etc. Some of these topics will be addressed in this chapter. The presentation of these topics is accompanied by the study of water quality data from the hydrological basin of the Vouga River and the Ria de Aveiro lagoon. In particular, statistical modelling is performed using data pertaining to the dissolved oxygen concentration variable (in mg/l) from the Carvoeiro water-monitoring site in the Vouga River basin. Section 2 discusses the area under study, while Section 3 presents a data descrip‐ tion with an exploratory analysis of the primary monitoring sites of the Vouga basin. Section 4 addresses the analysis of a time series through the decomposition into its main components and their treatment, while Section 5 presents the modelling of time series through a state space model approach

Neural-Kalman Schemes for Non-Stationary Channel Tracking and Learning

This Thesis focuses on channel tracking in Orthogonal Frequency-Division Multiplexing (OFDM), a widely-used method of data transmission in wireless communications, when abrupt changes occur in the channel. In highly mobile applications, new dynamics appear that might make channel tracking non-stationary, e.g. channels might vary with location, and location rapidly varies with time. Simple examples might be the di erent channel dynamics a train receiver faces when it is close to a station vs. crossing a bridge vs. entering a tunnel, or a car receiver in a route that grows more tra c-dense. Some of these dynamics can be modelled as channel taps dying or being reborn, and so tap birth-death detection is of the essence. In order to improve the quality of communications, we delved into mathematical methods to detect such abrupt changes in the channel, such as the mathematical areas of Sequential Analysis/ Abrupt Change Detection and Random Set Theory (RST), as well as the engineering advances in Neural Network schemes. This knowledge helped us nd a solution to the problem of abrupt change detection by informing and inspiring the creation of low-complexity implementations for real-world channel tracking. In particular, two such novel trackers were created: the Simpli- ed Maximum A Posteriori (SMAP) and the Neural-Network-switched Kalman Filtering (NNKF) schemes. The SMAP is a computationally inexpensive, threshold-based abrupt-change detector. It applies the three following heuristics for tap birth-death detection: a) detect death if the tap gain jumps into approximately zero (memoryless detection); b) detect death if the tap gain has slowly converged into approximately zero (memory detection); c) detect birth if the tap gain is far from zero. The precise parameters for these three simple rules can be approximated with simple theoretical derivations and then ne-tuned through extensive simulations. The status detector for each tap using only these three computationally inexpensive threshold comparisons achieves an error reduction matching that of a close-to-perfect path death/birth detection, as shown in simulations. This estimator was shown to greatly reduce channel tracking error in the target Signal-to-Noise Ratio (SNR) range at a very small computational cost, thus outperforming previously known systems. The underlying RST framework for the SMAP was then extended to combined death/birth and SNR detection when SNR is dynamical and may drift. We analyzed how di erent quasi-ideal SNR detectors a ect the SMAP-enhanced Kalman tracker's performance. Simulations showed SMAP is robust to SNR drift in simulations, although it was also shown to bene t from an accurate SNR detection. The core idea behind the second novel tracker, NNKFs, is similar to the SMAP, but now the tap birth/death detection will be performed via an arti cial neuronal network (NN). Simulations show that the proposed NNKF estimator provides extremely good performance, practically identical to a detector with 100% accuracy. These proposed Neural-Kalman schemes can work as novel trackers for multipath channels, since they are robust to wide variations in the probabilities of tap birth and death. Such robustness suggests a single, low-complexity NNKF could be reusable over di erent tap indices and communication environments. Furthermore, a di erent kind of abrupt change was proposed and analyzed: energy shifts from one channel tap to adjacent taps (partial tap lateral hops). This Thesis also discusses how to model, detect and track such changes, providing a geometric justi cation for this and additional non-stationary dynamics in vehicular situations, such as road scenarios where re ections on trucks and vans are involved, or the visual appearance/disappearance of drone swarms. An extensive literature review of empirically-backed abrupt-change dynamics in channel modelling/measuring campaigns is included. For this generalized framework of abrupt channel changes that includes partial tap lateral hopping, a neural detector for lateral hops with large energy transfers is introduced. Simulation results suggest the proposed NN architecture might be a feasible lateral hop detector, suitable for integration in NNKF schemes. Finally, the newly found understanding of abrupt changes and the interactions between Kalman lters and neural networks is leveraged to analyze the neural consequences of abrupt changes and brie y sketch a novel, abrupt-change-derived stochastic model for neural intelligence, extract some neuro nancial consequences of unstereotyped abrupt dynamics, and propose a new portfolio-building mechanism in nance: Highly Leveraged Abrupt Bets Against Failing Experts (HLABAFEOs). Some communication-engineering-relevant topics, such as a Bayesian stochastic stereotyper for hopping Linear Gauss-Markov (LGM) models, are discussed in the process. The forecasting problem in the presence of expert disagreements is illustrated with a hopping LGM model and a novel structure for a Bayesian stereotyper is introduced that might eventually solve such problems through bio-inspired, neuroscienti cally-backed mechanisms, like dreaming and surprise (biological Neural-Kalman). A generalized framework for abrupt changes and expert disagreements was introduced with the novel concept of Neural-Kalman Phenomena. This Thesis suggests mathematical (Neural-Kalman Problem Category Conjecture), neuro-evolutionary and social reasons why Neural-Kalman Phenomena might exist and found signi cant evidence for their existence in the areas of neuroscience and nance. Apart from providing speci c examples, practical guidelines and historical (out)performance for some HLABAFEO investing portfolios, this multidisciplinary research suggests that a Neural- Kalman architecture for ever granular stereotyping providing a practical solution for continual learning in the presence of unstereotyped abrupt dynamics would be extremely useful in communications and other continual learning tasks.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Luis Castedo Ribas.- Secretaria: Ana García Armada.- Vocal: José Antonio Portilla Figuera

VIVA: An Online Algorithm for Piecewise Curve Estimation Using ℓ\u3csup\u3e0\u3c/sup\u3e Norm Regularization

Many processes deal with piecewise input functions, which occur naturally as a result of digital commands, user interfaces requiring a confirmation action, or discrete-time sampling. Examples include the assembly of protein polymers and hourly adjustments to the infusion rate of IV fluids during treatment of burn victims. Estimation of the input is straightforward regression when the observer has access to the timing information. More work is needed if the input can change at unknown times. Successful recovery of the change timing is largely dependent on the choice of cost function minimized during parameter estimation. Optimal estimation of a piecewise input will often proceed by minimization of a cost function which includes an estimation error term (most commonly mean square error) and the number (cardinality) of input changes (number of commands). Because the cardinality (ℓ0 norm) is not convex, the ℓ2 norm (quadratic smoothing) and ℓ1 norm (total variation minimization) are often substituted because they permit the use of convex optimization algorithms. However, these penalize the magnitude of input changes and therefore bias the piecewise estimates. Another disadvantage is that global optimization methods must be run after the end of data collection. One approach to unbiasing the piecewise parameter fits would include application of total variation minimization to recover timing, followed by piecewise parameter fitting. Another method is presented herein: a dynamic programming approach which iteratively develops populations of candidate estimates of increasing length, pruning those proven to be dominated. Because the usage of input data is entirely causal, the algorithm recovers timing and parameter values online. A functional definition of the algorithm, which is an extension of Viterbi decoding and integrates the pruning concept from branch-and-bound, is presented. Modifications are introduced to improve handling of non-uniform sampling, non-uniform confidence, and burst errors. Performance tests using synthesized data sets as well as volume data from a research system recording fluid infusions show five-fold (piecewise-constant data) and 20-fold (piecewise-linear data) reduction in error compared to total variation minimization, along with improved sparsity and reduced sensitivity to the regularization parameter. Algorithmic complexity and delay are also considered

Kalman Filter Bibliography: Agriculture, Biology, and Medicine

27 pages, 1 article*Kalman Filter Bibliography: Agriculture, Biology, and Medicine* (Federer, Walter T.; Murty, B. R.) 27 page

Functionally Dissociable Influences on Learning Rate in a Dynamic Environment

Maintaining accurate beliefs in a changing environment requires dynamically adapting the rate at which one learns from new experiences. Beliefs should be stable in the face of noisy data but malleable in periods of change or uncertainty. Here we used computational modeling, psychophysics, and fMRI to show that adaptive learning is not a unitary phenomenon in the brain. Rather, it can be decomposed into three computationally and neuroanatomically distinct factors that were evident in human subjects performing a spatial-prediction task: (1) surprise-driven belief updating, related to BOLD activity in visual cortex; (2) uncertainty-driven belief updating, related to anterior prefrontal and parietal activity; and (3) reward-driven belief updating, a context-inappropriate behavioral tendency related to activity in ventral striatum. These distinct factors converged in a core system governing adaptive learning. This system, which included dorsomedial frontal cortex, responded to all three factors and predicted belief updating both across trials and across individuals