Multivariate time-series forecasting plays a crucial role in many real-world applications. It is a challenging problem as one needs to consider both intra-series temporal correlations and inter-series correlations simultaneously. Recently, there have been multiple works trying to capture both correlations, but most, if not all of them only capture temporal correlations in the time domain and resort to pre-defined priors as inter-series relationships. In this paper, we propose Spectral Temporal Graph Neural Network (StemGNN) to further improve the accuracy of multivariate time-series forecasting. StemGNN captures inter-series correlations and temporal dependencies \textit{jointly} in the \textit{spectral domain}. It combines Graph Fourier Transform (GFT) which models inter-series correlations and Discrete Fourier Transform (DFT) which models temporal dependencies in an end-to-end framework. After passing through GFT and DFT, the spectral representations hold clear patterns and can be predicted effectively by convolution and sequential learning modules. Moreover, StemGNN learns inter-series correlations automatically from the data without using pre-defined priors. We conduct extensive experiments on ten real-world datasets to demonstrate the effectiveness of StemGNN. Code is available at this https URL <<<

Given a multivariate time series, how can we forecast all of its variables efficiently and accurately? The multivariate forecasting, which is to predict the future observations of a multivariate time series, is a fundamental problem closely related to many real-world applications. However, previous multivariate models suffer from large model sizes due to the inefficiency of capturing complex intra-variable patterns and inter-variable correlations, resulting in poor accuracy. In this work, we propose AttnAR (attention-based autoregression), a novel approach for general multivariate forecasting which maximizes its model efficiency via separable structure. AttnAR first extracts variable-wise patterns by a mixed convolution extractor that efficiently combines deep convolution layers and shallow dense layers. Then, AttnAR aggregates the patterns by learning time-invariant attention maps between the target variables. AttnAR accomplishes the state-of-the-art forecasting accuracy in four datasets with up to 117.3 times fewer parameters than the best competitors. <<<

Multivariate time series (MTS) forecasting is widely used in various domains, such as meteorology and traffic. Due to limitations on data collection, transmission, and storage, real-world MTS data usually contains missing values, making it infeasible to apply existing MTS forecasting models such as linear regression and recurrent neural networks. Though many efforts have been devoted to this problem, most of them solely rely on local dependencies for imputing missing values, which ignores global temporal dynamics. Local dependencies/patterns would become less useful when the missing ratio is high, or the data have consecutive missing values; while exploring global patterns can alleviate such problem. Thus, jointly modeling local and global temporal dynamics is very promising for MTS forecasting with missing values. However, work in this direction is rather limited. Therefore, we study a novel problem of MTS forecasting with missing values by jointly exploring local and global temporal dynamics. We propose a new framework øurs, which leverages memory network to explore global patterns given estimations from local perspectives. We further introduce adversarial training to enhance the modeling of global temporal distribution. Experimental results on real-world datasets show the effectiveness of øurs for MTS forecasting with missing values and its robustness under various missing ratios. <<<

This paper introduces a new approach for Multivariate Time Series forecasting that jointly infers and leverages relations among time series. Its modularity allows it to be integrated with current univariate methods. Our approach allows to trade-off accuracy and computational efficiency gradually via offering on one extreme inference of a potentially fully-connected graph or on another extreme a bipartite graph. In the potentially fully-connected case we consider all pair-wise interactions among time-series which yields the best forecasting accuracy. Conversely, the bipartite case leverages the dependency structure by inter-communicating the N time series through a small set of K auxiliary nodes that we introduce. This reduces the time and memory complexity w.r.t. previous graph inference methods from O(N^2) to O(NK) with a small trade-off in accuracy. We demonstrate the effectiveness of our model in a variety of datasets where both of its variants perform better or very competitively to previous graph inference methods in terms of forecasting accuracy and time efficiency. <<<

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information. <<<

Because of the accessibility of big data collections from consumers, products, and stores, advanced sales forecasting capabilities have drawn great attention from many businesses, especially those in retail, because of the importance of forecasting in decision making. Improvement of forecasting accuracy, even by a small percentage, may have a substantial impact on companies’ production and financial planning, marketing strategies, inventory controls, and supply chain management. Specifically, our research goal is to forecast the sales of each product in each store in the near future. Motivated by tensor factorization methodologies for context-aware recommender systems, we propose a novel approach called the advanced temporal latent factor approach to sales forecasting, or ATLAS for short, which achieves accurate and individualized predictions for sales by building a single tensor factorization model across multiple stores and products. Our contribution is a combination of a tensor framework (to leverage information across stores and products), a new regularization function (to incorporate demand dynamics), and extrapolation of the tensor into future time periods using state-of-the-art statistical (seasonal autoregressive integrated moving-average models) and machine-learning (recurrent neural networks) models. The advantages of ATLAS are demonstrated on eight product category data sets collected by Information Resources, Inc., where we analyze a total of 165 million weekly sales transactions of over 15,560 products from more than 1,500 grocery stores. Summary of Contribution: Sales forecasting has been a task of long-standing importance. Accurate sales forecasting provides critical managerial implications for companies’ decision making and operations. Improvement of forecasting accuracy may have a substantial impact on companies’ production planning, marketing strategies, inventory controls, and supply chain management, among other things. This paper proposes a novel computational (machine-learning-based) approach to sales forecasting and thus is positioned directly at the intersection of computing and business/operations research. <<<

Rapid progress of industrial development, urbanization and traffic has caused air quality reduction that negatively affects human health and environmental sustainability, especially among developed countries. Numerous studies on the development of air quality forecasting model using machine learning have been conducted to control air pollution. As such, there are significant numbers of reviews on the application of machine learning in air quality forecasting. Shallow architectures of machine learning exhibit several limitations and yield lower forecasting accuracy than deep learning architecture. Deep learning is a new technology in computational intelligence; thus, its application in air quality forecasting is still limited. This study aims to investigate the deep learning applications in time series air quality forecasting. Owing to this, literature search is conducted thoroughly from all scientific databases to avoid unnecessary clutter. This study summarizes and discusses different types of deep learning algorithms applied in air quality forecasting, including the theoretical backgrounds, hyperparameters, applications and limitations. Hybrid deep learning with data decomposition, optimization algorithm and spatiotemporal models are also presented to highlight those techniques' effectiveness in tackling the drawbacks of individual deep learning models. It is clearly stated that hybrid deep learning was able to forecast future air quality with higher accuracy than individual models. At the end of the study, some possible research directions are suggested for future model development. The main objective of this review study is to provide a comprehensive literature summary of deep learning applications in time series air quality forecasting that may benefit interested researchers for subsequent research. <<<

Accompanying the rapid urbanization, many developing countries are suffering from serious air pollution problem. The demand for predicting future air quality is becoming increasingly more important to government's policy-making and people's decision making. In this paper, we predict the air quality of next 48 hours for each monitoring station, considering air quality data, meteorology data, and weather forecast data. Based on the domain knowledge about air pollution, we propose a deep neural network (DNN)-based approach (entitled DeepAir), which consists of a spatial transformation component and a deep distributed fusion network. Considering air pollutants' spatial correlations, the former component converts the spatial sparse air quality data into a consistent input to simulate the pollutant sources. The latter network adopts a neural distributed architecture to fuse heterogeneous urban data for simultaneously capturing the factors affecting air quality, e.g. meteorological conditions. We deployed DeepAir in our AirPollutionPrediction system, providing fine-grained air quality forecasts for 300+ Chinese cities every hour. The experimental results on the data from three-year nine Chinese-city demonstrate the advantages of DeepAir beyond 10 baseline methods. Comparing with the previous online approach in AirPollutionPrediction system, we have 2.4%, 12.2%, 63.2% relative accuracy improvements on short-term, long-term and sudden changes prediction, respectively. <<<

We propose a framework for general probabilistic multi-step time series regression. Specifically, we exploit the expressiveness and temporal nature of Sequence-to-Sequence Neural Networks (e.g. recurrent and convolutional structures), the nonparametric nature of Quantile Regression and the efficiency of Direct Multi-Horizon Forecasting. A new training scheme, *forking-sequences*, is designed for sequential nets to boost stability and performance. We show that the approach accommodates both temporal and static covariates, learning across multiple related series, shifting seasonality, future planned event spikes and cold-starts in real life large-scale forecasting. The performance of the framework is demonstrated in an application to predict the future demand of items sold on this http URL, and in a public probabilistic forecasting competition to predict electricity price and load. <<<

Probabilistic forecasting, i.e., estimating a time series’ future probability distribution given its past, is a key enabler for optimizing business processes. In retail businesses, for example, probabilistic demand forecasts are crucial for having the right inventory available at the right time and in the right place. This paper proposes DeepAR, a methodology for producing accurate probabilistic forecasts, based on training an autoregressive recurrent neural network model on a large number of related time series. We demonstrate how the application of deep learning techniques to forecasting can overcome many of the challenges that are faced by widely-used classical approaches to the problem. By means of extensive empirical evaluations on several real-world forecasting datasets, we show that our methodology produces more accurate forecasts than other state-of-the-art methods, while requiring minimal manual work. <<<

Forecasting is a common data science task that helps organizations with capacity planning, goal setting, and anomaly detection. Despite its importance, there are serious challenges associated with producing reliable and high quality forecasts — especially when there are a variety of time series and analysts with expertise in time series modeling are relatively rare. To address these challenges, we describe a practical approach to forecasting “at scale” that combines configurable models with analyst-in-the-loop performance analysis. We propose a modular regression model with interpretable parameters that can be intuitively adjusted by analysts with domain knowledge about the time series. We describe performance analyses to compare and evaluate forecasting procedures, and automatically flag forecasts for manual review and adjustment. Tools that help analysts to use their expertise most effectively enable reliable, practical forecasting of business time series. <<<

虽然空气污染是由污染物排放到大气中造成的,但是由于气象条件会影响污染物的扩散,因而实际观测到的污染水平会受到气象条件的影响.因此, 有效的空气质量管理要求污染评估指标和统计方法不受气象因素的干扰, 并能准确客观地反映污染物浓度的变化.为了评估北京地区潜在污染物排放的变化, 本文提出一种消除气象干扰的时空调整方法.通过控制气象条件, 调整后的污染物时空平均浓度可以捕捉到潜在排放量的变化.本文提出具体调整均值的方法, 并进行理论和数值分析,将此方法应用于北京地区的空气质量评估, 揭示一些有趣的模式和趋势, 这些结果可以用于空气质量评估和管理. <<<

连续性抽样调查由于能够描述目标总体随时间的动态变化过程,吸引了越来越多国内外学者的关注。国外连续性抽样的研究已经十分成熟,在已知的轮换模式下,建立合适的模型,使得模型能较好地描述数据的真实生成过程,从而得到精度更高的目标估计量。文章建立一般轮换模式rm1rm- 12下的时间序列模型,然后以6362模式为例,利用状态空间模型和卡尔曼滤波,给出已有信息下的最优估计,有效减少抽样误差,提高样本的估计精度。 <<<