Boosting Global Time Series Forecasting Models: A Two-Stage Modelling Framework

LoMEF: A framework to produce local explanations for global model time series forecasts

Novel approaches in Extended Principal Component Analysis to compare spatio-temporal patterns among multiple image time series

Forecasting time series data is an integral component for management, planning and decision making. Following the Big Data trend, large amounts of time series data are available from many heterogeneous data sources in more and more applications domains. The highly dynamic and often fluctuating character of these domains in combination with the logistic problems of collecting such data from a variety of sources, imposes new challenges to forecasting. Traditional approaches heavily rely on extensive and complete historical data to build time series models and are thus no longer applicable if time series are short or, even more important, intermittent. In addition, large numbers of time series have to be forecasted on different aggregation levels with preferably low latency, while forecast accuracy should remain high. This is almost impossible, when keeping the traditional focus on creating one forecast model for each individual time series. In this paper we tackle these challenges by presenting a novel forecasting approach called cross-sectional forecasting. This method is especially designed for Big Data sets with a multitude of time series. Our approach breaks with existing concepts by creating only one model for a whole set of time series and requiring only a fraction of the available data to provide accurate forecasts. By utilizing available data from all time series of a data set, missing values can be compensated and accurate forecasting results can be calculated quickly on arbitrary aggregation levels.

In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful basis vector for the set of data, and indicate which data use which basis vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the basis matrix, and the basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the basis matrix may not be smooth. We think that the basis vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, basis vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for basis vectors. However, the proposed method introduces the sparsity for coefficient vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient vectors and the smoothness for the basis vectors, can extract the smooth basis vectors and the original economical data are approximated as the weighted sum of the few bases vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.

Multiwavelets have recently been used for analysis of transient oscillations. Here we use them for transient oscillation detection by incorporating them into two existing Morlet-based self-normalizing detectors, one that operates on a single time series and another on two correlated time series. The Morlet-based detectors are effective in detecting weak, transient oscillations, especially in strong clutter where FFT based methods fail. Simulated receiver operating curves reveal that the new multiwavelet detectors show marked improvement when applied to complex, transient oscillations in white Gaussian noise and 60 dB clutter. At 0.1% false alarm rate for a (signal on) signal to noise ratio of 0.25, detection rates are: 95.5% and 99.6% for the single and dual time series detectors, respectively. These compare to 75% and 95.5% for the Morlet wavelet detectors.

The advent of a new generation of space-borne ocean colour sensors brings the prospect of global ocean measurements for decades into the future. These measurements will provide the basis for characterizing variability in the structure of the ocean's phytoplanktonic communities and the response of those communities to climatic change. In addition, the measurements will allow development of the scientific basis necessary to manage the sustainable resources of marine ecosystems. These studies will require a merged, long-term, multi-satellite ocean colour time series extending beyond the operational lifetimes of individual instruments. The Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) Project has been tasked to develop the tools required to create this time series. Among these tools are a comprehensive in situ (field collected) bio-optical dataset for validating ocean optics algorithms and associated models of oceanic properties; a programme to evaluate different atmospheric correction techniques; a programme to link the calibrations of individual satellite instruments; a programme to develop consistent calibration and validation datasets for satellite instruments; and a set of alternate methods to combine ocean colour measurements from different sources into a single time series. We report on the progress of this development work by the SIMBIOS Project.

Robust multivariate time series forecasting is crucial in many cyberphysical and Internet of Things applications. Existing state-of-the-art robust forecasting models decompose time series into independent functions covering trends and periodicities. However, these independent functions fail to capture correlations among multiple time series, thereby reducing prediction accuracy. Moreover, existing robust forecasting models treat certain abrupt but normal changes, e.g., caused by holidays, as outliers because they occur infrequently and have data distributions that resemble those of outliers. This exacerbates model bias and reduces prediction accuracy. This paper aims to capture correlations across multiple time series and abrupt but normal changes, thereby improving prediction accuracy. We employ weak labels to partition the dataset into source and target domains. Then, we propose the Domain Adversarial Robust Forecaster (DARF). This forecasting model is based on adversarial domain adaptation and includes two novel modules: Correlated Robust Forecaster (CORF) and Domain Critic. Specifically, CORF constitutes an encoder-decoder framework proficient at robust multivariate time series forecasting, and Domain Critic works to reduce data bias. Extensive experiments and discussions show that DARF is capable of state-of-the-art forecasting accuracy.

Forecasting ground-level irradiance over short horizons: Time series, meteorological, and time-varying parameter models

An enterprise service-level performance time series is a sequence of data points that quantify demand, throughput, average order-delivery time, quality of service, or end-to-end cost. Analytical and predictive models of such time series can be embedded into an enterprise information system (EIS) in order to provide meaningful insights into potential business problems and generate guidance for appropriate solutions. Time-series analysis includes periodicity detection, decomposition, and correlation analysis. Time-series prediction can be modeled as a regression problem to forecast a sequence of future time-series datapoints based on the given time series. The state-of-the-art (baseline) methods employed in time-series prediction generally apply advanced machine-learning algorithms. In this article, we propose a new univariate method for dealing with midterm time-series prediction. The proposed method first analyzes the hierarchical periodic structure in one time series and decomposes it into trend, season, and noise components. By discarding the noise component, the proposed method only focuses on predicting repetitive season and smoothed trend components. As a result, this method significantly improves upon the performance of baseline methods in midterm time-series prediction. Moreover, we propose a new multivariate method for dealing with short-term time-series prediction. The proposed method utilizes cross-correlation information derived from multiple time series. The amount of data taken from each time series for training the regression model is determined by results from hierarchical cross-correlation analysis. Such a data-filtering strategy leads to improved algorithm efficiency and prediction accuracy. By combining statistical methods with advanced machine-learning algorithms, we have achieved a significantly superior performance in both short-term and midterm time-series predictions compared to state-of-the-art (baseline) methods.

This work presents a novel approach to multivariate time series classification. The method exploits the multivariate structure of the time series and the possibilities of the stacking ensemble method. The basics of the method may be described in three steps: first, decomposing the multivariate time series on its constituent univariate time series; second, inducing a classifier for each univariate time series plus and additional multivariate classifier for the whole time series; third, creating the final multivariate time series classifier stacking the previous classifiers. The ensemble obtained has the potential to improve the accuracy of the single multivariate time series classifier. Several configurations of the stacking method have been tested on seven multivariate time series data sets. In five out of seven data sets, the proposed method obtains the smallest error rate. Moreover, in two out of seven data sets, stacking only the univariate time series classifiers provides the best results. The experimental results show that when a multivariate time series method does not produce an accurate classifier, stacking it with univariate time series classifiers is an alternative worthy of consideration.

Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting

SummaryTo quantify the major environmental drivers of stream bacterial population dynamics, we modelled temporal differences in stream bacterial communities to quantify community shifts, including those relating to cyclical seasonal variation and more sporadic bloom events. We applied Illumina MiSeq 16S rRNA bacterial gene sequencing of 892 stream biofilm samples, collected monthly for 36‐months from six streams. The streams were located a maximum of 118 km apart and drained three different catchment types (forest, urban and rural land uses). We identified repeatable seasonal patterns among bacterial taxa, allowing their separation into three ecological groupings, those following linear, bloom/trough and repeated, seasonal trends. Various physicochemical parameters (light, water and air temperature, pH, dissolved oxygen, nutrients) were linked to temporal community changes. Our models indicate that bloom events and seasonal episodes modify biofilm bacterial populations, suggesting that distinct microbial taxa thrive during these events including non‐cyanobacterial community members. These models could aid in determining how temporal environmental changes affect community assembly and guide the selection of appropriate statistical models to capture future community responses to environmental change.

Causality or driving in electrophysiological signal analysis

In the recent years, artificial intelligence techniques have attracted much attention in hydrological studies, while time series models are rarely used in this field. The present study evaluates the performance of artificial intelligence techniques including gene expression programming (GEP), Bayesian networks (BN), as well as time series models, namely autoregressive (AR) and autoregressive moving average (ARMA) for estimation of monthly streamflow. In addition, simple multiple linear regression (MLR) was also used. To fulfill this objective, the monthly streamflow data of Ponel and Toolelat stations located on Shafarood and Polrood Rivers, respectively in Northern Iran were used for the period of October 1964 to September 2014. In order to investigate the models’ accuracy, root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) were employed as the error statistics. The obtained results demonstrated that the single AR and ARMA time series models had better performance in comparison with the single GEP, BN and MLR methods. Furthermore, in this study, six hybrid models known as GEP-AR, GEP-ARMA, BN-AR, BN-ARMA, MLR-AR and MLR-ARMA were developed to enhance the estimation accuracy of the monthly streamflow. It was concluded that the developed hybrid models were more accurate than the corresponding single artificial intelligence and time series models. The obtained results confirmed that the integration of time series models and artificial intelligence techniques could be of use to improve the accuracy of single models in modeling purposes related to the hydrological studies.

В работе предложены математические модели прогнозирования нестационарных временных рядов с учётом внешних факторов и методы их структурной идентификации, основанные на совместном использовании многомерного варианта метода «Гусеница»-SSA и моделей SARIMAX, расширенных для прогнозирования временных рядов с несколькими сезонными составляющими и с учётом нескольких экзогенных переменных. Экспериментальные результаты показывают высокую эффективность предложенных моделей прогнозирования при выборе подходящих структурных параметров в сравнении с моделями SARIMAX.