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The starting point for much of multivariate analysis (MVA) is an $n\times p$ data matrix whose $n$ rows represent observations and whose $p$ columns represent variables. Some multivariate data sets, however, may be best conceptualized not…

Technological developments and open data policies have made large, global environmental datasets accessible to everyone. For analysing such datasets, including spatiotemporal correlations using traditional models based on Gaussian processes…

Multivariate time-series (MTS) forecasting is a paramount and fundamental problem in many real-world applications. The core issue in MTS forecasting is how to effectively model complex spatial-temporal patterns. In this paper, we develop a…

Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…

Time series data is prevalent across numerous fields, necessitating the development of robust and accurate forecasting models. Capturing patterns both within and between temporal and multivariate components is crucial for reliable…

Multivariate time series (MTS) forecasting has a wide range of applications in both industry and academia. Recently, spatial-temporal graph neural networks (STGNNs) have gained popularity as MTS forecasting methods. However, current STGNNs…

Multi-variate time series (MTS) data is a ubiquitous class of data abstraction in the real world. Any instance of MTS is generated from a hybrid dynamical system and their specific dynamics are usually unknown. The hybrid nature of such a…

Simple exponential smoothing is widely used in forecasting economic time series. This is because it is quick to compute and it generally delivers accurate forecasts. On the other hand, its multivariate version has received little attention…

Unsupervised fault detection in multivariate time series plays a vital role in ensuring the stable operation of complex systems. Traditional methods often assume that normal data follow a single Gaussian distribution and identify anomalies…

Multivariate time series classification (TSC) is critical for various applications in fields such as healthcare and finance. While various approaches for TSC have been explored, important properties of time series, such as shift…

Traditional solar flare forecasting approaches have mostly relied on physics-based or data-driven models using solar magnetograms, treating flare predictions as a point-in-time classification problem. This approach has limitations,…

High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…

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…

In this article, we introduce the mean independent component analysis for multivariate time series to reduce the parameter space. In particular, we seek for a contemporaneous linear transformation that detects univariate mean independent…

This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…

For Multivariate Time Series Forecasting (MTSF), recent deep learning applications show that univariate models frequently outperform multivariate ones. To address the difficiency in multivariate models, we introduce a method to Construct…

In the present paper we investigate methods related to both the Singular Spectrum Analysis (SSA) and subspace-based methods in signal processing. We describe common and specific features of these methods and consider different kinds of…

In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…

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…

Errors are common in time series due to unreliable sensor measurements. Existing methods focus on univariate data but do not utilize the correlation between dimensions. Cleaning each dimension separately may lead to a less accurate result,…