Spatial Time-Series Modeling: A review of the proposed methodologies

This paper discusses three modelling techniques, which apply to multiple time series data that correspond to different spatial locations (spatial time series). The first two methods, namely the Space-Time ARIMA (STARIMA) and the Bayesian Vector Autoregressive (BVAR) model with spatial priors apply when interest lies on the spatio-temporal evolution of a single variable. The former is better suited for applications of large spatial and temporal dimension whereas the latter can be realistically performed when the number of locations of the study is rather small. Next, we consider models that aim to describe relationships between variables with a spatio-temporal reference and discuss the general class of dynamic space-time models in the framework presented by Elhorst (2001). Each model class is introduced through a motivating application.spatial time-series, space-time models, STARIMA, Bayesian Vector Autoregressions

Forecasting Intraday Time Series with Multiple Seasonal Cycles Using Parsimonious Seasonal Exponential Smoothing

This paper concerns the forecasting of seasonal intraday time series. An extension of Holt-Winters exponential smoothing has been proposed that smoothes an intraday cycle and an intraweek cycle. A recently proposed exponential smoothing method involves smoothing a different intraday cycle for each distinct type of day of the week. Similar days are allocated identical intraday cycles. A limitation is that the method allows only whole days to be treated as identical. We introduce an exponential smoothing formulation that allows parts of different days of the week to be treated as identical. The result is a method that involves the smoothing and initialisation of fewer terms than the other two exponential smoothing methods. We evaluate forecasting up to a day ahead using two empirical studies. For electricity load data, the new method compares well with a range of alternatives. The second study involves a series of arrivals at a call centre that is open for a shorter duration at the weekends than on weekdays. By contrast with the previously proposed exponential smoothing methods, our new method can model in a straightforward way this situation, where the number of periods on each day of the week is not the same.Exponential smoothing; Intraday data; Electricity load; Call centre arrivals.

Time is of the Essence: Machine Learning-based Intrusion Detection in Industrial Time Series Data

The Industrial Internet of Things drastically increases connectivity of devices in industrial applications. In addition to the benefits in efficiency, scalability and ease of use, this creates novel attack surfaces. Historically, industrial networks and protocols do not contain means of security, such as authentication and encryption, that are made necessary by this development. Thus, industrial IT-security is needed. In this work, emulated industrial network data is transformed into a time series and analysed with three different algorithms. The data contains labeled attacks, so the performance can be evaluated. Matrix Profiles perform well with almost no parameterisation needed. Seasonal Autoregressive Integrated Moving Average performs well in the presence of noise, requiring parameterisation effort. Long Short Term Memory-based neural networks perform mediocre while requiring a high training- and parameterisation effort.Comment: Extended version of a publication in the 2018 IEEE International Conference on Data Mining Workshops (ICDMW

Network Filtering of Spatial-temporal GNN for Multivariate Time-series Prediction

We propose an architecture for multivariate time-series prediction that integrates a spatial-temporal graph neural network with a filtering module which filters the inverse correlation matrix into a sparse network structure. In contrast with existing sparsification methods adopted in graph neural networks, our model explicitly leverages time-series filtering to overcome the low signal-to-noise ratio typical of complex systems data. We present a set of experiments, where we predict future sales volume from a synthetic time-series sales volume dataset. The proposed spatial-temporal graph neural network displays superior performances to baseline approaches with no graphical information, fully connected, disconnected graphs, and unfiltered graphs, as well as the state-of-the-art spatial-temporal GNN. Comparison of the results with Diffusion Convolutional Recurrent Neural Network (DCRNN) suggests that, by combining a (inferior) GNN with graph sparsification and filtering, one can achieve comparable or better efficacy than the state-of-the-art in multivariate time-series regression

A Hydropower Facility as an Energy Water Signal Processor

In recent times, various efforts have been made to address the challenge of adequately representing hydropower systems in modeling frameworks, accounting for the lack of data to represent the multiple constraints in hydropower operation. This research is a pilot data-driven methodology for characterizing, classifying, and comparing the water-to-energy and energy-to-water signal transformations that hydropower facilities as signal processors accomplish. In this study, a Box Jenkins transfer function/noise model is used to identify the relationship between reservoir inflows and outflows. For examining the feasibility of this methodology, 5-minute fleet data for five storage and five run-of-river facilities was provided by the Tennessee Valley Authority (TVA) and transfer function models are developed. The influence of past inflow and outflow values on the current outflow decisions was investigated and summarized by examining the results of Box Jenkins methodology. Finally, dominance analysis was introduced to add value to the Box Jenkins model results and provide different stakeholders with a set of concepts to convey the functionality of hydropower

Performance modelling with adaptive hidden Markov models and discriminatory processor sharing queues

In modern computer systems, workload varies at different times and locations. It is important to model the performance of such systems via workload models that are both representative and efficient. For example, model-generated workloads represent realistic system behaviour, especially during peak times, when it is crucial to predict and address performance bottlenecks. In this thesis, we model performance, namely throughput and delay, using adaptive models and discrete queues. Hidden Markov models (HMMs) parsimoniously capture the correlation and burstiness of workloads with spatiotemporal characteristics. By adapting the batch training of standard HMMs to incremental learning, online HMMs act as benchmarks on workloads obtained from live systems (i.e. storage systems and financial markets) and reduce time complexity of the Baum-Welch algorithm. Similarly, by extending HMM capabilities to train on multiple traces simultaneously it follows that workloads of different types are modelled in parallel by a multi-input HMM. Typically, the HMM-generated traces verify the throughput and burstiness of the real data. Applications of adaptive HMMs include predicting user behaviour in social networks and performance-energy measurements in smartphone applications. Equally important is measuring system delay through response times. For example, workloads such as Internet traffic arriving at routers are affected by queueing delays. To meet quality of service needs, queueing delays must be minimised and, hence, it is important to model and predict such queueing delays in an efficient and cost-effective manner. Therefore, we propose a class of discrete, processor-sharing queues for approximating queueing delay as response time distributions, which represent service level agreements at specific spatiotemporal levels. We adapt discrete queues to model job arrivals with distributions given by a Markov-modulated Poisson process (MMPP) and served under discriminatory processor-sharing scheduling. Further, we propose a dynamic strategy of service allocation to minimise delays in UDP traffic flows whilst maximising a utility function.Open Acces

On the Modeling of CO2 EUA and CER Prices of EU-ETS for the 2008–2012 Period

Increased consumption of fossil fuels in industrial production has led to a significant elevation in the emission of greenhouse gases and to global warming. The most effective international action against global warming is the Kyoto Protocol, which aims to reduce carbon emissions to desired levels in a certain time span. Carbon trading is one of the mechanisms used to achieve the desired reductions. One of the most important implications of carbon trading for industrial systems is the risk of uncertainty about the prices of carbon allowance permits traded in the carbon markets. In this paper, we consider stochastic and time series modeling of carbon market prices and provide estimates of the model parameters involved, based on the European Union emissions trading scheme carbon allowances data obtained for 2008–2012 period. In particular, we consider fractional Brownian motion and autoregressive moving average–generalized autoregressive conditional heteroskedastic modeling of the European Union emissions trading scheme data and provide comparisons with benchmark models. Our analysis reveals evidence for structural changes in the underlying models in the span of the years 2008–2012. Data-driven methods for identifying possible change-points in the underlying models are employed, and a detailed analysis is provided. Our analysis indicated change-points in the European Union Allowance (EUA) prices in the first half of 2009 and in the second half of 2011, whereas in the Certified Emissions Reduction (CER) prices three change-points have appeared, in the first half of 2009, the middle of 2011, and in the second half of 2012. These change-points seem to parallel the global economic indicators as well. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd

Optimal Short-Term Forecast for Locally Stationary Functional Time Series

Accurate curve forecasting is of vital importance for policy planning, decision making and resource allocation in many engineering and industrial applications. In this paper we establish a theoretical foundation for the optimal short-term linear prediction of non-stationary functional or curve time series with smoothly time-varying data generating mechanisms. The core of this work is to establish a unified functional auto-regressive approximation result for a general class of locally stationary functional time series. A double sieve expansion method is proposed and theoretically verified for the asymptotic optimal forecasting. A telecommunication traffic data set is used to illustrate the usefulness of the proposed theory and methodology