The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear estimation, we describe the theoretical framework and then we provide detailed examples of response distributions, including binomial, Poisson, negative binomial, geometric, normal, log-normal, gamma, exponential, Weibull, Pareto, beta, and inverse Gaussian. We give numerical illustrations for all distributions (except for the normal). Putting together all the above distributions, we give a unified Bayesian approach to non-Gaussian time series analysis, with applications from finance and medicine to biology and the behavioural sciences. Throughout the models we discuss Bayesian forecasting and, for each model, we derive the multi-step forecast mean. Finally, we describe model assessment using the likelihood function, and Bayesian model monitoring.
Accurate forecasting of the U.K. gross value added (GVA) is fundamental for measuring the growth of the U.K. economy. A common nonstationarity in GVA data, such as the ABML series, is its increase in variance over time due to inflation. Transformed or inflation-adjusted series can still be challenging for classical stationarity-assuming forecasters. We adopt a different approach that works directly with the GVA series by advancing recent forecasting methods for locally stationary time series. Our approach results in more accurate and reliable forecasts, and continues to work well even when the…
This paper develops forecasting methodology and application of new classes of dynamic models for time series of non-negative counts. Novel univariate models synthesise dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models allow use of dynamic covariates in both binary and non-zero count components. Sequential Bayesian analysis allows fast, parallel analysis of sets of decoupled time series. New multivariate models then enable information sharing in contexts when data at a more highly aggregated level pr…
Time series forecasting plays an increasingly important role in modern business decisions. In today's data-rich environment, people often aim to choose the optimal forecasting model for their data. However, identifying the optimal model requires professional knowledge and experience, making accurate forecasting a challenging task. To mitigate the importance of model selection, we propose a simple and reliable algorithm to improve the forecasting performance. Specifically, we construct multiple time series with different sub-seasons from the original time series. These derived series highlight …
Accurate travel products price forecasting is a highly desired feature that allows customers to take informed decisions about purchases, and companies to build and offer attractive tour packages. Thanks to machine learning (ML), it is now relatively cheap to develop highly accurate statistical models for price time-series forecasting. However, once models are deployed in production, it is their monitoring, maintenance and improvement which carry most of the costs and difficulties over time. We introduce a data-driven framework to continuously monitor and maintain deployed time-series forecasti…
Univariate time series often take the form of a collection of curves observed sequentially over time. Examples of these include hourly ground-level ozone concentration curves. These curves can be viewed as a time series of functions observed at equally spaced intervals over a dense grid. Since functional time series may contain various types of outliers, we introduce a robust functional time series forecasting method to down-weigh the influence of outliers in forecasting. Through a robust principal component analysis based on projection pursuit, a time series of functions can be decomposed int…
We discuss model and forecast combination in time series forecasting. A foundational Bayesian perspective based on agent opinion analysis theory defines a new framework for density forecast combination, and encompasses several existing forecast pooling methods. We develop a novel class of dynamic latent factor models for time series forecast synthesis; simulation-based computation enables implementation. These models can dynamically adapt to time-varying biases, miscalibration and inter-dependencies among multiple models or forecasters. A macroeconomic forecasting study highlights the dynamic …
A new forecasting method based on the concept of the profile predictive the likelihood function is proposed for discrete-valued processes. In particular, generalized autoregressive and moving average (GARMA) models for Poisson distributed data are explored in details. Highest density regions are used to construct forecasting regions. The proposed forecast estimates and regions are coherent. Large sample results are derived for the forecasting distribution. Numerical studies using simulations and a real data set are used to establish the performance of the proposed forecasting method. Robustnes…
Combining forecast from different models has shown to perform better than single forecast in most time series. To improve the quality of forecast we can go for combining forecast. We study the effect of decomposing a series into multiple components and performing forecasts on each component separately... The original series is decomposed into trend, seasonality and an irregular component for each series. The statistical methods such as ARIMA, Holt-Winter have been used to forecast these components. In this paper we focus on how the best models of one series can be applied to similar frequency …
I overview recent research advances in Bayesian state-space modeling of multivariate time series. A main focus is on the decouple/recouple concept that enables application of state-space models to increasingly large-scale data, applying to continuous or discrete time series outcomes. The scope includes large-scale dynamic graphical models for forecasting and multivariate volatility analysis in areas such as economics and finance, multi-scale approaches for forecasting discrete/count time series in areas such as commercial sales and demand forecasting, and dynamic network flow models for areas …
Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. However, the forecasting performance of such functional time series models may be affected by the presence of outlying observations which are very common in many scientific fields. Outliers may distort the functional time series model structure, and thus…
We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Previous definitions of dynamic principal components depend on past and future values of the series. For this reason, they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this paper can be successfully used for forecasting high-dimensional multiple time series. An alternating least squares algorithm to compute the proposed ODPC is presented. We prove…
We consider forecasting the latent rate profiles of a time series of inhomogeneous Poisson processes. The work is motivated by operations management of queueing systems, in particular, telephone call centers, where accurate forecasting of call arrival rates is a crucial primitive for efficient staffing of such centers. Our forecasting approach utilizes dimension reduction through a factor analysis of Poisson variables, followed by time series modeling of factor score series. Time series forecasts of factor scores are combined with factor loadings to yield forecasts of future Poisson rate profi…
A novel method for predicting time series is described and demonstrated. This method inputs time series data points and outputs multiple "spaghetti" functions from which predictions can be made. Spaghetti prediction has desirable properties that are not realized by classic autoregression, moving average, spline, Gaussian process, and other methods. It is particularly appropriate for short time series because it allows asymmetric prediction distributions and produces prediction functions which are robust in that they use multiple independent models.
Optimal starting point for time series forecasting
School of Statistics and Mathematics, Central University of Finance and Economics（中央财经大学统计与数学学院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Smart Campus Construction Center, Central University of Finance and Economics（中央财经大学智慧校园建设中心）；Guanghua School of Management, Peking University（北京大学光华管理学院）；School of Statistics, Beijing Normal University（北京师范大学统计学院）
An approach is presented for making predictions about functional time series. The method is applied to data coming from periodically correlated processes and electricity demand, obtaining accurate point forecasts and narrow prediction bands that cover high proportions of the forecasted functional datum, for a given confidence level. The method is computationally efficient and substantially different to other functional time series methods, offering a new insight for the analysis of these data structures.
Many methods for time-series forecasting are known in classical statistics, such as autoregression, moving averages, and exponential smoothing. The DeepAR framework is a novel, recent approach for time-series forecasting based on deep learning. DeepAR has shown very promising results already. However, time series often have change points, which can degrade the DeepAR's prediction performance substantially. This paper extends the DeepAR framework by detecting and including those change points. We show that our method performs as well as standard DeepAR when there are no change points and consid…
With the advent of Big Data, nowadays in many applications databases containing large quantities of similar time series are available. Forecasting time series in these domains with traditional univariate forecasting procedures leaves great potentials for producing accurate forecasts untapped. Recurrent neural networks (RNNs), and in particular Long Short-Term Memory (LSTM) networks, have proven recently that they are able to outperform state-of-the-art univariate time series forecasting methods in this context when trained across all available time series. However, if the time series database …
Université Libre de Bruxelles（布鲁塞尔自由大学）；Cairo University（开罗大学）
Multi-step ahead forecasting is still an open challenge in time series forecasting. Several approaches that deal with this complex problem have been proposed in the literature but an extensive comparison on a large number of tasks is still missing. This paper aims to fill this gap by reviewing existing strategies for multi-step ahead forecasting and comparing them in theoretical and practical terms. To attain such an objective, we performed a large scale comparison of these different strategies using a large experimental benchmark (namely the 111 series from the NN5 forecasting competition). I…
Kaunas University of Technology（考纳斯理工大学）；Rivile（Rivile私人有限责任公司）
Amounts of historical data collected increase and business intelligence applicability with automatic forecasting of time series are in high demand. While no single time series modeling method is universal to all types of dynamics, forecasting using an ensemble of several methods is often seen as a compromise. Instead of fixing ensemble diversity and size, we propose to predict these aspects adaptively using meta-learning. Meta-learning here considers two separate random forest regression models, built on 390 time-series features, to rank 22 univariate forecasting methods and recommend ensemble…
Monash University（莫纳什大学）；University of Sydney（悉尼大学）
Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algo…
Time series forecasting is difficult. It is difficult even for recurrent neural networks with their inherent ability to learn sequentiality. This article presents a recurrent neural network based time series forecasting framework covering feature engineering, feature importances, point and interval predictions, and forecast evaluation. The description of the method is followed by an empirical study using both LSTM and GRU networks.
In this paper, we present a new approach to time series forecasting. Time series data are prevalent in many scientific and engineering disciplines. Time series forecasting is a crucial task in modeling time series data, and is an important area of machine learning. In this work we developed a novel method that employs Transformer-based machine learning models to forecast time series data. This approach works by leveraging self-attention mechanisms to learn complex patterns and dynamics from time series data. Moreover, it is a generic framework and can be applied to univariate and multivariate …
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；School of Management, Xi'an Jiaotong University（西安交通大学管理学院）
A new variational mode decomposition (VMD) based deep learning approach is proposed in this paper for time series forecasting problem. Firstly, VMD is adopted to decompose the original time series into several sub-signals. Then, a convolutional neural network (CNN) is applied to learn the reconstruction patterns on the decomposed sub-signals to obtain several reconstructed sub-signals. Finally, a long short term memory (LSTM) network is employed to forecast the time series with the decomposed sub-signals and the reconstructed sub-signals as inputs. The proposed VMD-CNN-LSTM approach is origina…
In this paper we offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting. We begin by describing possible formulations of the problem and offer commentary on related topics and challenges in obtaining globally optimal solutions. Key theorems are provided, and the paper closes with some expository examples.
NTT Communication Science Laboratories（NTT通信科学实验室）；NTT Software Innovation Center（NTT软件创新中心）
Time-series forecasting is important for many applications. Forecasting models are usually trained using time-series data in a specific target task. However, sufficient data in the target task might be unavailable, which leads to performance degradation. In this paper, we propose a few-shot learning method that forecasts a future value of a time-series in a target task given a few time-series in the target task. Our model is trained using time-series data in multiple training tasks that are different from target tasks. Our model uses a few time-series to build a forecasting function based on a…
Monash University（莫纳什大学）；University of Melbourne（墨尔本大学）
In the current context of Big Data, the nature of many forecasting problems has changed from predicting isolated time series to predicting many time series from similar sources. This has opened up the opportunity to develop competitive global forecasting models that simultaneously learn from many time series. But, it still remains unclear when global forecasting models can outperform the univariate benchmarks, especially along the dimensions of the homogeneity/heterogeneity of series, the complexity of patterns in the series, the complexity of forecasting models, and the lengths/number of seri…
We participated in the M4 competition for time series forecasting and describe here our methods for forecasting daily time series. We used an ensemble of five statistical forecasting methods and a method that we refer to as the correlator. Our retrospective analysis using the ground truth values published by the M4 organisers after the competition demonstrates that the correlator was responsible for most of our gains over the naive constant forecasting method. We identify data leakage as one reason for its success, partly due to test data selected from different time intervals, and partly due …
By significant improvements in modern electrical systems, planning for unit commitment and power dispatching of them are two big concerns between the researchers. Short-term load forecasting plays a significant role in planning and dispatching them. In recent years, numerous works have been done on Short-term load forecasting. Having an accurate model for predicting the load can be beneficial for optimizing the electrical sources and protecting energy. Several models such as Artificial Intelligence and Statistics model have been used to improve the accuracy of load forecasting. Among the stati…
George Washington University（乔治华盛顿大学）；Shandong University（山东大学）；Beihang University（北京航空航天大学）
Time series forecasting is a key component in many industrial and business decision processes and recurrent neural network (RNN) based models have achieved impressive progress on various time series forecasting tasks. However, most of the existing methods focus on single-task forecasting problems by learning separately based on limited supervised objectives, which often suffer from insufficient training instances. As the Transformer architecture and other attention-based models have demonstrated its great capability of capturing long term dependency, we propose two self-attention based sharing…
Beihang University（北京航空航天大学）；Central University of Finance and Economics（中央财经大学）
Feature-based time series representations have attracted substantial attention in a wide range of time series analysis methods. Recently, the use of time series features for forecast model averaging has been an emerging research focus in the forecasting community. Nonetheless, most of the existing approaches depend on the manual choice of an appropriate set of features. Exploiting machine learning methods to extract features from time series automatically becomes crucial in state-of-the-art time series analysis. In this paper, we introduce an automated approach to extract time series features …
In this work, we propose an ensemble forecasting approach based on randomized neural networks. Improved randomized learning streamlines the fitting abilities of individual learners by generating network parameters in accordance with the data and target function features. A pattern-based representation of time series makes the proposed approach suitable for forecasting time series with multiple seasonality. We propose six strategies for controlling the diversity of ensemble members. Case studies conducted on four real-world forecasting problems verified the effectiveness and superior performanc…
Forecasting models that are trained across sets of many time series, known as Global Forecasting Models (GFM), have shown recently promising results in forecasting competitions and real-world applications, outperforming many state-of-the-art univariate forecasting techniques. In most cases, GFMs are implemented using deep neural networks, and in particular Recurrent Neural Networks (RNN), which require a sufficient amount of time series to estimate their numerous model parameters. However, many time series databases have only a limited number of time series. In this study, we propose a novel, …
In this paper, we propose two nonparametric methods used in the forecasting of functional time-dependent data, namely functional singular spectrum analysis recurrent forecasting and vector forecasting. Both algorithms utilize the results of functional singular spectrum analysis and past observations in order to predict future data points where recurrent forecasting predicts one function at a time and the vector forecasting makes predictions using functional vectors. We compare our forecasting methods to a gold standard algorithm used in the prediction of functional, time-dependent data by way …
In the context of time series forecasting, it is a common practice to evaluate multiple methods and choose one of these methods or an ensemble for producing the best forecasts. However, choosing among different ensembles over multiple methods remains a challenging task that undergoes a combinatorial explosion as the number of methods increases. In the context of demand forecasting or revenue forecasting, this challenge is further exacerbated by a large number of time series as well as limited historical data points available due to changing business context. Although deep learning forecasting …
Central University of Finance and Economics（中央财经大学）；Beijing Wuzi University（北京物资学院）
Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pat…
Kohonen self-organisation maps are a well know classification tool, commonly used in a wide variety of problems, but with limited applications in time series forecasting context. In this paper, we propose a forecasting method specifically designed for multi-dimensional long-term trends prediction, with a double application of the Kohonen algorithm. Practical applications of the method are also presented.
IIT（意大利理工学院）；UCL（伦敦大学学院）；Amazon Web Services（亚马逊云服务）
While classical time series forecasting considers individual time series in isolation, recent advances based on deep learning showed that jointly learning from a large pool of related time series can boost the forecasting accuracy. However, the accuracy of these methods suffers greatly when modeling out-of-sample time series, significantly limiting their applicability compared to classical forecasting methods. To bridge this gap, we adopt a meta-learning view of the time series forecasting problem. We introduce a novel forecasting method, called Meta Global-Local Auto-Regression (Meta-GLAR), t…
Deep learning based forecasting methods have become the methods of choice in many applications of time series prediction or forecasting often outperforming other approaches. Consequently, over the last years, these methods are now ubiquitous in large-scale industrial forecasting applications and have consistently ranked among the best entries in forecasting competitions (e.g., M4 and M5). This practical success has further increased the academic interest to understand and improve deep forecasting methods. In this article we provide an introduction and overview of the field: We present importan…
Point forecasting of univariate time series is a challenging problem with extensive work having been conducted. However, nonparametric probabilistic forecasting of time series, such as in the form of quantiles or prediction intervals is an even more challenging problem. In an effort to expand the possible forecasting paradigms we devise and explore an extrapolation-based approach that has not been applied before for probabilistic forecasting. We present a novel quantile Fourier neural network is for nonparametric probabilistic forecasting of univariate time series. Multi-step predictions are p…
Time series forecasting has gained lots of attention recently; this is because many real-world phenomena can be modeled as time series. The massive volume of data and recent advancements in the processing power of the computers enable researchers to develop more sophisticated machine learning algorithms such as neural networks to forecast the time series data. In this paper, we propose various neural network architectures to forecast the time series data using the dynamic measurements; moreover, we introduce various architectures on how to combine static and dynamic measurements for forecastin…
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；IBM Almaden Research Center（IBM阿尔马登研究中心）
Sparse and irregularly sampled multivariate time series are common in clinical, climate, financial and many other domains. Most recent approaches focus on classification, regression or forecasting tasks on such data. In forecasting, it is necessary to not only forecast the right value but also to forecast when that value will occur in the irregular time series. In this work, we present an approach to forecast not only the values but also the time at which they are expected to occur.
PALO ALTO NETWORKS（帕洛阿尔托网络公司）；ADVANCED APPLIED AI RESEARCH（高级应用人工智能研究院）
Time series forecasting is a fundamental task emerging from diverse data-driven applications. Many advanced autoregressive methods such as ARIMA were used to develop forecasting models. Recently, deep learning based methods such as DeepAr, NeuralProphet, Seq2Seq have been explored for time series forecasting problem. In this paper, we propose a novel time series forecast model, DeepGB. We formulate and implement a variant of Gradient boosting wherein the weak learners are DNNs whose weights are incrementally found in a greedy manner over iterations. In particular, we develop a new embedding ar…
Cyber-physical systems often consist of entities that interact with each other over time. Meanwhile, as part of the continued digitization of industrial processes, various sensor technologies are deployed that enable us to record time-varying attributes (a.k.a., time series) of such entities, thus producing correlated time series. To enable accurate forecasting on such correlated time series, this paper proposes two models that combine convolutional neural networks (CNNs) and recurrent neural networks (RNNs). The first model employs a CNN on each individual time series, combines the convoluted…
AI Institute（人工智能研究院）；Shanghai Jiao Tong University（上海交通大学）
Probabilistic time series forecasting involves estimating the distribution of future based on its history, which is essential for risk management in downstream decision-making. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks and the dependency is modeled by recurrent neural nets. We take the automatic relevance determination (ARD) view and devise a network to exploit the exogenous variables in addition to time series. In particular, our ARD network can incorporate the uncertai…
Machine learning methods trained on raw numerical time series data exhibit fundamental limitations such as a high sensitivity to the hyper parameters and even to the initialization of random weights. A combination of a recurrent neural network with a dimension-reducing symbolic representation is proposed and applied for the purpose of time series forecasting. It is shown that the symbolic representation can help to alleviate some of the aforementioned problems and, in addition, might allow for faster training without sacrificing the forecast performance.
Long Short-Term Memory (LSTM) networks are often used to capture temporal dependency patterns. By stacking multi-layer LSTM networks, it can capture even more complex patterns. This paper explores the effectiveness of applying stacked LSTM networks in the time series prediction domain, specifically, the traffic volume forecasting. Being able to predict traffic volume more accurately can result in better planning, thus greatly reduce the operation cost and improve overall efficiency.
Time Series Forecasting is at the core of many practical applications such as sales forecasting for business, rainfall forecasting for agriculture and many others. Though this problem has been extensively studied for years, it is still considered a challenging problem due to complex and evolving nature of time series data. Typical methods proposed for time series forecasting modeled linear or non-linear dependencies between data observations. However it is a generally accepted notion that no one method is universally effective for all kinds of time series data. Attempts have been made to use d…
Numerous deep learning architectures have been developed to accommodate the diversity of time series datasets across different domains. In this article, we survey common encoder and decoder designs used in both one-step-ahead and multi-horizon time series forecasting -- describing how temporal information is incorporated into predictions by each model. Next, we highlight recent developments in hybrid deep learning models, which combine well-studied statistical models with neural network components to improve pure methods in either category. Lastly, we outline some ways in which deep learning c…
Middle East Technical University（中东技术大学）；Massachusetts Institute of Technology（麻省理工学院）
Many applications in different domains produce large amount of time series data. Making accurate forecasting is critical for many decision makers. Various time series forecasting methods exist which use linear and nonlinear models separately or combination of both. Studies show that combining of linear and nonlinear models can be effective to improve forecasting performance. However, some assumptions that those existing methods make, might restrict their performance in certain situations. We provide a new Autoregressive Integrated Moving Average (ARIMA)-Artificial Neural Network(ANN) hybrid me…
Time series modeling and forecasting has fundamental importance to various practical domains. Thus a lot of active research works is going on in this subject during several years. Many important models have been proposed in literature for improving the accuracy and effectiveness of time series forecasting. The aim of this dissertation work is to present a concise description of some popular time series forecasting models used in practice, with their salient features. In this thesis, we have described three important classes of time series models, viz. the stochastic, neural networks and SVM ba…
