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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), that adapts to each time series by learning in closed-form the mapping from the representations produced by a recurrent neural network (RNN) to one-step-ahead forecasts. Crucially, the parameters ofthe RNN are learned across multiple time series by backpropagating through the closed-form adaptation mechanism. In our extensive empirical evaluation we show that our method is competitive with the state-of-the-art in out-of-sample forecasting accuracy reported in earlier work.

Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of these joint quantile regressions, however, is \textit{quantile crossing}, which violates the desirable monotone property of the conditional quantile function. In this work, we propose the Incremental (Spline) Quantile Functions I(S)QF, a flexible and efficient distribution-free quantile estimation framework that resolves quantile crossing with a simple neural network layer. Moreover, I(S)QF inter/extrapolate to predict arbitrary quantile levels that differ from the underlying training ones. Equipped with the analytical evaluation of the continuous ranked probability score of I(S)QF representations, we apply our methods to NN-based times series forecasting cases, where the savings of the expensive re-training costs for non-trained quantile levels is particularly significant. We also provide a generalization error analysis of our proposed approaches under the sequence-to-sequence setting. Lastly, extensive experiments demonstrate the improvement of consistency and accuracy errors over other baselines.

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 different sub-seasonal patterns of the original series, making it possible for the forecasting methods to capture diverse patterns and components of the data. Subsequently, we produce forecasts for these multiple series separately with classical statistical models (ETS or ARIMA). Finally, the forecasts are combined. We evaluate our approach on widely-used forecasting competition data sets (M1, M3, and M4) in terms of both point forecasts and prediction intervals. We observe performance improvements compared with the benchmarks. Our approach is particularly suitable and robust for the data with higher frequency. To demonstrate the practical value of our proposition, we showcase the performance improvements from our approach on hourly load data that exhibit multiple seasonal patterns.

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the art point forecasting methods.

Stock trend forecasting, aiming at predicting the stock future trends, is crucial for investors to seek maximized profits from the stock market. Many event-driven methods utilized the events extracted from news, social media, and discussion board to forecast the stock trend in recent years. However, existing event-driven methods have two main shortcomings: 1) overlooking the influence of event information differentiated by the stock-dependent properties; 2) neglecting the effect of event information from other related stocks. In this paper, we propose a relational event-driven stock trend forecasting (REST) framework, which can address the shortcoming of existing methods. To remedy the first shortcoming, we propose to model the stock context and learn the effect of event information on the stocks under different contexts. To address the second shortcoming, we construct a stock graph and design a new propagation layer to propagate the effect of event information from related stocks. The experimental studies on the real-world data demonstrate the efficiency of our REST framework. The results of investment simulation show that our framework can achieve a higher return of investment than baselines.

Traffic forecasting is an important factor for the success of intelligent transportation systems. Deep learning models including convolution neural networks and recurrent neural networks have been applied in traffic forecasting problems to model the spatial and temporal dependencies. In recent years, to model the graph structures in the transportation systems as well as the contextual information, graph neural networks (GNNs) are introduced as new tools and have achieved the state-of-the-art performance in a series of traffic forecasting problems. In this survey, we review the rapidly growing body of recent research using different GNNs, e.g., graph convolutional and graph attention networks, in various traffic forecasting problems, e.g., road traffic flow and speed forecasting, passenger flow forecasting in urban rail transit systems, demand forecasting in ride-hailing platforms, etc. We also present a collection of open data and source resources for each problem, as well as future research directions. To the best of our knowledge, this paper is the first comprehensive survey that explores the application of graph neural networks for traffic forecasting problems. We have also created a public Github repository to update the latest papers, open data and source resources.

Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, such as quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a $ProbSparse$ Self-attention mechanism, which achieves $O(L \log L)$ in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.

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.

Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of modeling complex patterns or dependencies lying in real word data. To address such concerns, various deep learning models, mainly Recurrent Neural Network (RNN) based methods, are proposed. Nevertheless, capturing extremely long-term patterns while effectively incorporating information from other variables remains a challenge for time-series forecasting. Furthermore, lack-of-explainability remains one serious drawback for deep neural network models. Inspired by Memory Network proposed for solving the question-answering task, we propose a deep learning based model named Memory Time-series network (MTNet) for time series forecasting. MTNet consists of a large memory component, three separate encoders, and an autoregressive component to train jointly. Additionally, the attention mechanism designed enable MTNet to be highly interpretable. We can easily tell which part of the historic data is referenced the most.