A.1 Time Series Forecasting We first briefly review the related literature of time series forecasting (TSF) methods as below. Complex temporal patterns can be manifested over short-and long-term as the time series evolves across time. To leverage the time evolution nature, existing statistical models, such as ARIMA [6] and Gaussian process regression [7] have been well established and applied to many downstream tasks [28, 29, 2]. Recurrent neural network (RNN) models are also introduced to model temporal dependencies for TSF in a sequence-to-sequence paradigm [24, 9, 61, 40, 46, 50, 53]. Besides, temporal attention [49, 59, 56] and causal convolution [3, 5, 54] are further explored to model the intrinsic temporal dependencies.

The explosion of Time Series (TS) data, driven by advancements in technology, necessitates sophisticated analytical methods. Modern management systems increasingly rely on analyzing this data, highlighting the importance of effcient processing techniques. State-of-the-art Machine Learning (ML) approaches for TS analysis and forecasting are becoming prevalent. This paper briefly describes and compiles suitable algorithms for TS regression task. We compare these algorithms against each other and the classic ARIMA method using diverse datasets: complete data, data with outliers, and data with missing values. The focus is on forecasting accuracy, particularly for long-term predictions. This research aids in selecting the most appropriate algorithm based on forecasting needs and data characteristics.

This thesis studies the effectiveness of Long Short Term Memory model in forecasting future Job Openings and Labor Turnover Survey data in the United States. Drawing on multiple economic indicators from various sources, the data are fed directly into LSTM model to predict JOLT job openings in subsequent periods. The performance of the LSTM model is compared with conventional autoregressive approaches, including ARIMA, SARIMA, and Holt-Winters. Findings suggest that the LSTM model outperforms these traditional models in predicting JOLT job openings, as it not only captures the dependent variables trends but also harmonized with key economic factors. These results highlight the potential of deep learning techniques in capturing complex temporal dependencies in economic data, offering valuable insights for policymakers and stakeholders in developing data-driven labor market strategies

In this section, we will give an overview of the related literature in time series forecasting. Traditional Time Series Models The first generation of well-discussed time series model is the autoregressive family. ARIMA Box & Jenkins (1968); Box & Pierce (1970) follows the Markov process and build recursive sequential forecasting. However, a plain autoregressive process has difficulty in dealing non-stationary sequences. Thus, ARIMA employed a pre-process iteration by differencing, which transforms the series to stationary. Still, ARIMA and related models have the linear assumption in the autoregressive process, which limits their usage in complex forecasting tasks. Deep Neural Network in Forecasting With the bloom of deep neural networks, recurrent neural networks (RNNs) were designed for tasks involving sequential data.

Traffic monitoring is a cornerstone of effective network management and cybersecurity, providing Internet Service Providers (ISPs) with critical insights to detect anomalies, mitigate congestion, and maintain network performance [1]. The surge in video streaming, cloud computing, and online gaming is driving rapid growth in internet usage, contributing to increasingly complex and less predictable network traffic. Efficient network monitoring allows ISPs to maintain service quality, mitigate security risks, and optimize bandwidth in real time [2]. However, real-time monitoring alone is insufficient for proactively managing network resources. To anticipate variations in demand and prevent service disruptions, ISPs increasingly adopt advanced forecasting techniques to predict traffic patterns and optimize resource allocation in advance [3]. Accurate traffic forecasting allows ISPs to efficiently allocate resources, scale network capacity, and sustain service quality under fluctuating loads [3]. The rise of diverse, high-bandwidth services has significantly increased network traffic variability. Traditional models like ARIMA and exponential smoothing, which assume linearity, struggle with ISP data due to prevalent non-linear and high-frequency fluctuations, especially during peak traffic hours [4]. These limitations have driven the adoption of deep learning models, particularly neural networks, which excel at capturing complex temporal dependencies across various forecasting domains [5].

Effective epidemic modeling is essential for managing public health crises, requiring robust methods to predict disease spread and optimize resource allocation. This study introduces a novel deep learning framework that advances time series forecasting for infectious diseases, with its application to COVID 19 data as a critical case study. Our hybrid approach integrates Convolutional Neural Networks (CNNs) and Long Short Term Memory (LSTM) models to capture spatial and temporal dynamics of disease transmission across diverse regions. The CNN extracts spatial features from raw epidemiological data, while the LSTM models temporal patterns, yielding precise and adaptable predictions. To maximize performance, we employ a hybrid optimization strategy combining the Whale Optimization Algorithm (WOA) and Gray Wolf Optimization (GWO) to fine tune hyperparameters, such as learning rates, batch sizes, and training epochs enhancing model efficiency and accuracy. Applied to COVID 19 case data from 24 countries across six continents, our method outperforms established benchmarks, including ARIMA and standalone LSTM models, with statistically significant gains in predictive accuracy (e.g., reduced RMSE). This framework demonstrates its potential as a versatile method for forecasting epidemic trends, offering insights for resource planning and decision making in both historical contexts, like the COVID 19 pandemic, and future outbreaks.

Container terminals, pivotal nodes in the network of empty container movement, hold significant potential for enhancing operational efficiency within terminal depots through effective collaboration between transporters and terminal operators. This collaboration is crucial for achieving optimization, leading to streamlined operations and reduced congestion, thereby benefiting both parties. Consequently, there is a pressing need to develop the most suitable forecasting approaches to address this challenge. This study focuses on developing and evaluating a data-driven approach for forecasting empty container availability at container terminal depots within a Vehicle Booking System (VBS) framework. It addresses the gap in research concerning optimizing empty container dwell time and aims to enhance operational efficiencies in container terminal operations. Four forecasting models-Naive, ARIMA, Prophet, and LSTM-are comprehensively analyzed for their predictive capabilities, with LSTM emerging as the top performer due to its ability to capture complex time series patterns. The research underscores the significance of selecting appropriate forecasting techniques tailored to the specific requirements of container terminal operations, contributing to improved operational planning and management in maritime logistics.

Anomaly detection in time series data is a well-studied problem due to its importance in detecting faults, intrusions, and unusual events in critical systems [1, 3]. Extensive surveys have reviewed methods for general anomaly detection [1], outlier analysis [3], and specifically for temporal data [4]. Despite this progress, accurately identifying anomalies in time series remains challenging [14]. A key difficulty is that anomalies are often sparse--comprising only a tiny fraction of observations [2]. This extreme class imbalance makes it hard for models to recognize anomalies without producing many false alarms [6]. One strategy to detect anomalies is to forecast future behavior and flag deviations between predictions and actual values [15, 16]. Classical forecasting models, such as ARIMA [12] and exponential smoothing, as well as decomposition-based methods like Prophet [13], have been applied to model normal time series patterns and identify outliers when residuals exceed a threshold. Numerous other approaches leverage deep generative models (e.g., variational autoencoders [17], GANs [18]) or attention mechanisms [19] to improve multivariate time series anomaly detection. However, most prior methods treat multivariate time series as an unstructured collection of variables, not accounting for known relationships among them.

--The increasing complexity of supply chains and the rising costs associated with defective or substandard goods ("bad goods") highlight the urgent need for advanced predictive methodologies to mitigate risks and enhance operational efficiency. This research presents a novel framework that integrates Time Series ARIMA (AutoRegressive Integrated Moving A ver-age) models with a proprietary formula specifically designed to calculate bad goods after time series forecasting. ARIMA is employed to capture temporal trends in time series data, while the newly developed formula quantifies the likelihood and impact of defects with greater precision. Experimental results, validated on a dataset spanning 2022-2024 for Organic Beer-G 1 Liter, demonstrate that the proposed method outperforms traditional statistical models, such as Exponential Smoothing and Holt-Winters, in both prediction accuracy and risk evaluation. I. INTRODUCTION In modern industrial systems, detecting and preventing defective or substandard products--termed "bad goods"--such as manufacturing flaws or spoiled items like Organic Beer-G 1 Liter, remains a critical challenge. These defects result in financial losses, reputational harm, and supply chain inefficiencies. Traditional approaches like statistical process control and manual inspections struggle to address the complexity of large-scale operations [1]. The advent of big data and advanced analytics has elevated predictive methods as a key strategy for preempting such risks [2].

In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these problems as generative-adversarial (i.e., min-max) optimization problems, for which we develop polynomial-time algorithms to solve, the former of which relies on an exact first-order oracle, and the latter, a stochastic one. We extend our approach to solve inverse multiagent simulacral learning in polynomial time and number of samples. In these problems, we seek a simulacrum, meaning parameters and an associated equilibrium that replicate the given observations in expectation. We find that our approach outperforms the widely-used ARIMA method in predicting prices in Spanish electricity markets based on time-series data.