Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last five years have proposed diverse sets of objective loss functions to address cases such as biased data, long-term forecasting, multicollinear features, etc. In this paper, we have summarized 14 well-known regression loss functions commonly used for time series forecasting and listed out the circumstances where their application can aid in faster and better model convergence. We have also demonstrated how certain categories of loss functions perform well across all data sets and can be considered as a baseline objective function in circumstances where the distribution of the data is unknown. Our code is available at GitHub: https://github.com/aryan-jadon/Regression-Loss-Functions-in-Time-Series-Forecasting-Tensorflow.

目标变量的日志和平方根变换通常用于预测模型中，以预测未来的销售。这些转换通常会导致更好的性能模型。但是，他们还引入了系统的负面偏见（遗产不足）。在本文中，我们证明了这种偏见的存在，深入研究其根本原因，并引入了两种方法以纠正偏见。我们得出的结论是，提出的偏差校正方法提高了模型性能（最多可提高50％），并为将偏置校正纳入建模工作流程而提高。我们还尝试了“ Tweedie”成本功能家族，这些功能通过直接建模销售来规避转换偏见问题。我们得出的结论是，Tweedie回归在建模销售时迄今为止提供了最佳性能，使其成为使用变换的目标变量的强大替代方案。

With the evolution of power systems as it is becoming more intelligent and interactive system while increasing in flexibility with a larger penetration of renewable energy sources, demand prediction on a short-term resolution will inevitably become more and more crucial in designing and managing the future grid, especially when it comes to an individual household level. Projecting the demand for electricity for a single energy user, as opposed to the aggregated power consumption of residential load on a wide scale, is difficult because of a considerable number of volatile and uncertain factors. This paper proposes a customized GRU (Gated Recurrent Unit) and Long Short-Term Memory (LSTM) architecture to address this challenging problem. LSTM and GRU are comparatively newer and among the most well-adopted deep learning approaches. The electricity consumption datasets were obtained from individual household smart meters. The comparison shows that the LSTM model performs better for home-level forecasting than alternative prediction techniques-GRU in this case. To compare the NN-based models with contrast to the conventional statistical technique-based model, ARIMA based model was also developed and benchmarked with LSTM and GRU model outcomes in this study to show the performance of the proposed model on the collected time series data.

急诊部门（EDS）是葡萄牙国家卫生服务局的基本要素，可作为具有多样化和非常严重医疗问题的用户的切入点。由于ED的固有特征；预测使用服务的患者数量特别具有挑战性。富裕和医疗专业人员人数之间的不匹配可能会导致提供的服务质量下降，并造成对整个医院产生影响的问题，并从其他部门征用医疗保健工作者以及推迟手术。 。 ED人满为患的部分是由非紧急患者驱动的，尽管没有医疗紧急情况，但诉诸于紧急服务，几乎占每日患者总数的一半。本文描述了一种新颖的深度学习体系结构，即时间融合变压器，该结构使用日历和时间序列协变量来预测预测间隔和4周期间的点预测。我们得出的结论是，可以预测葡萄牙健康区域（HRA）（HRA）的平均绝对百分比误差（MAPE）和均方根误差（RMSE）为84.4102人/天的平均绝对百分比误差（MAPE）。本文显示了支持使用静态和时间序列协变量的多元方法的经验证据，同时超越了文献中常见的其他模型。

本文介绍了一个集成预测方法，通过减少特征和模型选择假设来显示M4Competitiation数据集的强劲结果，称为甜甜圈（不利用人为假设）。我们的假设减少，主要由自动生成的功能和更多样化的集合模型组成，显着优于Montero-Manso等人的统计特征的集合方法FForma。 （2020）。此外，我们用长短期内存网络（LSTM）AutoEncoder调查特征提取，并发现此类特征包含传统统计特征方法未捕获的重要信息。合奏加权模型使用LSTM功能和统计功能准确地结合模型。特征重要性和交互的分析表明，单独的统计数据的LSTM特征略有优势。聚类分析表明，不同的基本LSTM功能与大多数统计特征不同。我们还发现，通过使用新模型增强合奏来增加加权模型的解决方案空间是加权模型学习使用的东西，解释了准确性的一部分。最后，我们为集合的最佳组合和选择提供了正式的前后事实分析，通过M4数据集的线性优化量化差异。我们还包括一个简短的证据，模型组合优于模型选择，后者。

预测组合在预测社区中蓬勃发展，近年来，已经成为预测研究和活动主流的一部分。现在，由单个（目标）系列产生的多个预测组合通过整合来自不同来源收集的信息，从而提高准确性，从而减轻了识别单个“最佳”预测的风险。组合方案已从没有估计的简单组合方法演变为涉及时间变化的权重，非线性组合，组件之间的相关性和交叉学习的复杂方法。它们包括结合点预测和结合概率预测。本文提供了有关预测组合的广泛文献的最新评论，并参考可用的开源软件实施。我们讨论了各种方法的潜在和局限性，并突出了这些思想如何随着时间的推移而发展。还调查了有关预测组合实用性的一些重要问题。最后，我们以当前的研究差距和未来研究的潜在见解得出结论。

在医疗保健系统中，需要患者使用可穿戴设备进行远程数据收集和对健康数据的实时监控以及健康状况的状态。可穿戴设备的这种采用导致收集和传输的数据量显着增加。由于设备由较小的电池电源运行，因此由于设备的高处理要求以进行数据收集和传输，因此可以快速减少它们。鉴于医疗数据的重要性，必须所有传输数据遵守严格的完整性和可用性要求。减少医疗保健数据的量和传输频率将通过使用推理算法改善设备电池寿命。有一个以准确性和效率改善传输指标的问题，彼此之间的权衡，例如提高准确性会降低效率。本文表明，机器学习可用于分析复杂的健康数据指标，例如数据传输的准确性和效率，以使用Levenberg-Marquardt算法来克服权衡问题，从而增强这两个指标，从而通过少较少的样本来传输，同时保持维护准确性。使用标准心率数据集测试该算法以比较指标。结果表明，LMA最好以3.33倍的效率进行样本数据尺寸和79.17％的精度，在7种不同的采样案例中具有相似的准确性，用于测试，但表明效率提高。与具有高效率的现有方法相比，这些提出的方法使用机器学习可以显着改善两个指标，而无需牺牲其他指标。

间歇时间序列的分层预测是研究和实证研究中的挑战。庞大的研究侧重于提高每个层次结构的准确性，尤其是底部层次的间歇时间序列。然后，在每个层次结构上调和预测，以进一步提高整体性能。在本文中，我们提出了一种与分层对准方法的预测，该方法将底部水平预测视为可变的柔和预测，以确保在层次结构的上层上的预测精度。我们采用纯深度学习预测方法的N- BEATS对高层的连续时间序列和广泛使用的基于树的算法LightGBM为底层间歇时间序列。具有对准方法的分层预测是自下而上方法的简单且有效的变体，其占难以观察到底部水平的偏差。它允许在较低级别的次优预测保留更高的整体性能。该研究在本实证研究中由第一作者在M5预测准确性竞争期间开发，排名第二。该方法也是良好的商业战略规划有益。

预测意大利电负载的整个24轮廓的问题被寻址为多任务学习问题，其复杂性通过替代正则化方法保持控制。鉴于四分之一小时的采样，使用96个预测器，每个预测器都在线性地取决于96个回归量。 96x96矩阵重量形成96x96矩阵，可以看到并显示为在方域上采样的表面。探讨了降低表面自由度的不同正则化和稀疏方法，比较了所获得的预测与意大利传输系统操作员泰尔纳的预测。除了在四分之一小时意味着绝对百分比误差和平均绝对误差方面表现出艰难的替代，预测残差与Terna略微相关，这表明进一步改进可以随着预测聚集而产生进一步的改进。事实上，聚合预测在四分之一小时和每日平均值百分比误差方面产生了进一步的相关液滴，而是在考虑的三个测试年度上平均误差和根均值误差（高达30％）。

预测基金绩效对投资者和基金经理都是有益的，但这是一项艰巨的任务。在本文中，我们测试了深度学习模型是否比传统统计技术更准确地预测基金绩效。基金绩效通常通过Sharpe比率进行评估，该比例代表了风险调整的绩效，以确保基金之间有意义的可比性。我们根据每月收益率数据序列数据计算了年度夏普比率，该数据的时间序列数据为600多个投资于美国上市大型股票的开放式共同基金投资。我们发现，经过现代贝叶斯优化训练的长期短期记忆（LSTM）和封闭式复发单元（GRUS）深度学习方法比传统统计量相比，预测基金的Sharpe比率更高。结合了LSTM和GRU的预测的合奏方法，可以实现所有模型的最佳性能。有证据表明，深度学习和结合能提供有希望的解决方案，以应对基金绩效预测的挑战。

电力行业正在大力实施智能网格技术，以提高可靠性，可用性，安全性和效率。该实施需要技术进步，标准和法规的发展以及测试和计划。智能电网载荷预测和管理对于降低需求波动和改善连接发电机，分销商和零售商的市场机制至关重要。在政策实施或外部干预措施中，有必要分析其对电力需求的影响的不确定性，以使系统对需求的波动更加准确。本文分析了外部干预的不确定性对电力需求的影响。它实现了一种结合概率和全局预测模型的框架，使用深度学习方法来估计干预措施的因果影响分布。通过预测受影响实例的反事实分布结果，然后将其与实际结果进行对比来评估因果效应。我们将COVID-19锁定对能源使用的影响视为评估这种干预对电力需求分布的不均匀影响的案例研究。我们可以证明，在澳大利亚和某些欧洲国家的最初封锁期间，槽通常比峰值更大的下降，而平均值几乎不受影响。

我们向Facebook先知推出了一位继任者，为可解释，可扩展和用户友好的预测框架制定了一个行业标准。随着时间序列数据的扩散，可说明的预测仍然是企业和运营决策的具有挑战性的任务。需要混合解决方案来弥合可解释的古典方法与可扩展深层学习模型之间的差距。我们将先知视为这样一个解决方案的前兆。然而，先知缺乏本地背景，这对于预测近期未来至关重要，并且由于其斯坦坦后代而挑战。 NeultProphet是一种基于Pytorch的混合预测框架，并用标准的深度学习方法培训，开发人员可以轻松扩展框架。本地上下文使用自动回归和协变量模块引入，可以配置为经典线性回归或作为神经网络。否则，NeultProphet保留了先知的设计理念，提供了相同的基本模型组件。我们的结果表明，NeultProcrophet在一组生成的时间序列上产生了相当或优质的质量的可解释的预测组件。 NeultProphet在各种各样的现实数据集合中占先知。对于中期预测，NeultProclecrophet将预测精度提高55％至92％。

PV power forecasting models are predominantly based on machine learning algorithms which do not provide any insight into or explanation about their predictions (black boxes). Therefore, their direct implementation in environments where transparency is required, and the trust associated with their predictions may be questioned. To this end, we propose a two stage probabilistic forecasting framework able to generate highly accurate, reliable, and sharp forecasts yet offering full transparency on both the point forecasts and the prediction intervals (PIs). In the first stage, we exploit natural gradient boosting (NGBoost) for yielding probabilistic forecasts, while in the second stage, we calculate the Shapley additive explanation (SHAP) values in order to fully comprehend why a prediction was made. To highlight the performance and the applicability of the proposed framework, real data from two PV parks located in Southern Germany are employed. Comparative results with two state-of-the-art algorithms, namely Gaussian process and lower upper bound estimation, manifest a significant increase in the point forecast accuracy and in the overall probabilistic performance. Most importantly, a detailed analysis of the model's complex nonlinear relationships and interaction effects between the various features is presented. This allows interpreting the model, identifying some learned physical properties, explaining individual predictions, reducing the computational requirements for the training without jeopardizing the model accuracy, detecting possible bugs, and gaining trust in the model. Finally, we conclude that the model was able to develop complex nonlinear relationships which follow known physical properties as well as human logic and intuition.

信息爆炸的时代促使累积巨大的时间序列数据，包括静止和非静止时间序列数据。最先进的算法在处理静止时间数据方面取得了体面的性能。然而，解决静止​​时间系列的传统算法不适用于外汇交易的非静止系列。本文调查了适用的模型，可以提高预测未来非静止时间序列序列趋势的准确性。特别是，我们专注于识别潜在模型，并调查识别模式从历史数据的影响。我们提出了基于RNN的\ Rebuttal {The} SEQ2Seq模型的组合，以及通过动态时间翘曲和Zigzag峰谷指示器提取的注重机制和富集的集合特征。定制损失函数和评估指标旨在更加关注预测序列的峰值和谷点。我们的研究结果表明，我们的模型可以在外汇数据集中预测高精度的4小时未来趋势，这在逼真的情况下至关重要，以协助外汇交易决策。我们进一步提供了对各种损失函数，评估指标，模型变体和组件对模型性能的影响的评估。

The cyber-physical convergence is opening up new business opportunities for industrial operators. The need for deep integration of the cyber and the physical worlds establishes a rich business agenda towards consolidating new system and network engineering approaches. This revolution would not be possible without the rich and heterogeneous sources of data, as well as the ability of their intelligent exploitation, mainly due to the fact that data will serve as a fundamental resource to promote Industry 4.0. One of the most fruitful research and practice areas emerging from this data-rich, cyber-physical, smart factory environment is the data-driven process monitoring field, which applies machine learning methodologies to enable predictive maintenance applications. In this paper, we examine popular time series forecasting techniques as well as supervised machine learning algorithms in the applied context of Industry 4.0, by transforming and preprocessing the historical industrial dataset of a packing machine's operational state recordings (real data coming from the production line of a manufacturing plant from the food and beverage domain). In our methodology, we use only a single signal concerning the machine's operational status to make our predictions, without considering other operational variables or fault and warning signals, hence its characterization as ``agnostic''. In this respect, the results demonstrate that the adopted methods achieve a quite promising performance on three targeted use cases.

In time series forecasting, decomposition-based algorithms break aggregate data into meaningful components and are therefore appreciated for their particular advantages in interpretability. Recent algorithms often combine machine learning (hereafter ML) methodology with decomposition to improve prediction accuracy. However, incorporating ML is generally considered to sacrifice interpretability inevitably. In addition, existing hybrid algorithms usually rely on theoretical models with statistical assumptions and focus only on the accuracy of aggregate predictions, and thus suffer from accuracy problems, especially in component estimates. In response to the above issues, this research explores the possibility of improving accuracy without losing interpretability in time series forecasting. We first quantitatively define interpretability for data-driven forecasts and systematically review the existing forecasting algorithms from the perspective of interpretability. Accordingly, we propose the W-R algorithm, a hybrid algorithm that combines decomposition and ML from a novel perspective. Specifically, the W-R algorithm replaces the standard additive combination function with a weighted variant and uses ML to modify the estimates of all components simultaneously. We mathematically analyze the theoretical basis of the algorithm and validate its performance through extensive numerical experiments. In general, the W-R algorithm outperforms all decomposition-based and ML benchmarks. Based on P50_QL, the algorithm relatively improves by 8.76% in accuracy on the practical sales forecasts of JD.com and 77.99% on a public dataset of electricity loads. This research offers an innovative perspective to combine the statistical and ML algorithms, and JD.com has implemented the W-R algorithm to make accurate sales predictions and guide its marketing activities.

传染病仍然是全世界人类疾病和死亡的主要因素之一，其中许多疾病引起了流行的感染波。特定药物和预防疫苗防止大多数流行病的不可用，这使情况变得更糟。这些迫使公共卫生官员，卫生保健提供者和政策制定者依靠由流行病的可靠预测产生的预警系统。对流行病的准确预测可以帮助利益相关者调整对手的对策，例如疫苗接种运动，人员安排和资源分配，以减少手头的情况，这可以转化为减少疾病影响的影响。不幸的是，大多数过去的流行病（例如，登革热，疟疾，肝炎，流感和最新的Covid-19）表现出非线性和非平稳性特征，这是由于它们基于季节性依赖性变化以及这些流行病的性质的扩散波动而引起的。 。我们使用基于最大的重叠离散小波变换（MODWT）自动回归神经网络分析了各种流行时期时间序列数据集，并将其称为EWNET。 MODWT技术有效地表征了流行时间序列中的非平稳行为和季节性依赖性，并在拟议的集合小波网络框架中改善了自回旋神经网络的预测方案。从非线性时间序列的角度来看，我们探讨了所提出的EWNET模型的渐近平稳性，以显示相关的马尔可夫链的渐近行为。我们还理论上还研究了学习稳定性的效果以及在拟议的EWNET模型中选择隐藏的神经元的选择。从实际的角度来看，我们将我们提出的EWNET框架与以前用于流行病预测的几种统计，机器学习和深度学习模型进行了比较。

In this paper, we propose a new short-term load forecasting (STLF) model based on contextually enhanced hybrid and hierarchical architecture combining exponential smoothing (ES) and a recurrent neural network (RNN). The model is composed of two simultaneously trained tracks: the context track and the main track. The context track introduces additional information to the main track. It is extracted from representative series and dynamically modulated to adjust to the individual series forecasted by the main track. The RNN architecture consists of multiple recurrent layers stacked with hierarchical dilations and equipped with recently proposed attentive dilated recurrent cells. These cells enable the model to capture short-term, long-term and seasonal dependencies across time series as well as to weight dynamically the input information. The model produces both point forecasts and predictive intervals. The experimental part of the work performed on 35 forecasting problems shows that the proposed model outperforms in terms of accuracy its predecessor as well as standard statistical models and state-of-the-art machine learning models.

时间序列预测是重要的应用领域的核心，对机器学习算法构成了重大挑战。最近，神经网络体系结构已广泛应用于时间序列的预测问题。这些模型中的大多数都是通过最大程度地减少损失函数来衡量预测偏离实际值的训练的。典型的损耗函数包括均方根误差（MSE）和平均绝对误差（MAE）。在存在噪声和不确定性的情况下，神经网络模型倾向于复制时间序列的最后观察值，从而限制了它们对现实数据的适用性。在本文中，我们提供了上述问题的形式定义，还提供了观察到问题的预测的一些示例。我们还提出了一个正规化项，对先前看到的值的复制进行了惩罚。我们在合成数据集和现实世界数据集上评估了拟议的正规化项。我们的结果表明，正则化项会在一定程度上缓解上述问题，并产生更健壮的模型。

Dengue fever is a virulent disease spreading over 100 tropical and subtropical countries in Africa, the Americas, and Asia. This arboviral disease affects around 400 million people globally, severely distressing the healthcare systems. The unavailability of a specific drug and ready-to-use vaccine makes the situation worse. Hence, policymakers must rely on early warning systems to control intervention-related decisions. Forecasts routinely provide critical information for dangerous epidemic events. However, the available forecasting models (e.g., weather-driven mechanistic, statistical time series, and machine learning models) lack a clear understanding of different components to improve prediction accuracy and often provide unstable and unreliable forecasts. This study proposes an ensemble wavelet neural network with exogenous factor(s) (XEWNet) model that can produce reliable estimates for dengue outbreak prediction for three geographical regions, namely San Juan, Iquitos, and Ahmedabad. The proposed XEWNet model is flexible and can easily incorporate exogenous climate variable(s) confirmed by statistical causality tests in its scalable framework. The proposed model is an integrated approach that uses wavelet transformation into an ensemble neural network framework that helps in generating more reliable long-term forecasts. The proposed XEWNet allows complex non-linear relationships between the dengue incidence cases and rainfall; however, mathematically interpretable, fast in execution, and easily comprehensible. The proposal's competitiveness is measured using computational experiments based on various statistical metrics and several statistical comparison tests. In comparison with statistical, machine learning, and deep learning methods, our proposed XEWNet performs better in 75% of the cases for short-term and long-term forecasting of dengue incidence.