We prove that a time series satisfying a (linear) multivariate autoregressive moving average (VARMA) model satisfies the same model assumption in the reversed time direction, too, if all innovations are normally distributed. This reversibility breaks down if the innovations are non-Gaussian. This means that under the assumption of a VARMA process with nonGaussian noise, the arrow of time become...

Spectral analysis considers the problem of determining (the art of recovering) the spectral content (i.e., the distribution of power over frequency) of a stationary time series from a finite set of measurements, by means of either nonparametric or parametric techniques. This paper introduces the spectral analysis problem, motivates the definition of power spectral density functions, and reviews...

Multivariate time series prediction is a critical problem that encountered in many fields, and recurrent neural network (RNN)-based approaches have been widely used to address this problem. However, traditional RNN-based for predicting multivariate are still facing challenges, as often related each other historical observations real-world applications. To limitation, paper proposes spatiotempor...

Deep time series metric learning is challenging due to the difficult trade-off between temporal invariance nonlinear distortion and discriminative power in identifying non-matching sequences. This paper proposes a novel neural network-based approach for robust yet classification verification. adapts parameterized attention model warping greater more adaptive invariance. It against not only loca...

Multivariate time series forecasting has long been a subject of great concern. For example, there are many valuable applications in electricity consumption, solar power generation, traffic congestion, finance, and so on. Accurately periodic data such as can greatly improve the reliability tasks engineering applications. Time problems often modeled using deep learning methods. However, informati...