Latent adversarial regularized autoencoder for high-dimensional probabilistic time series prediction

Many practical applications require probabilistic prediction of time series to model the distribution on future horizons. With ever-increasing dimensions, much effort has been invested into developing methods that often make an assumption about the independence between time series. Consequently, the probabilistic prediction in high-dimensional environments has become an essential topic with significant challenges. In this paper, we propose a novel probabilistic model called latent adversarial regularized autoencoder, abbreviated as TimeLAR, specifically for high-dimensional multivariate Time Series Prediction (TSP). It integrates the flexibility of Generative Adversarial Networks (GANs) and the capability of autoencoders in extracting higher-level non-linear features. Through flexible autoencoder mapping, TimeLAR learns cross-series relationships and encodes this global information into several latent variables. We design a modified Transformer for these latent variables to capture global temporal patterns and infer latent space prediction distributions, where only one step is required to output multi-step predictions. Furthermore, we employ the GAN to further refine the performance of latent space predictions, by using a discriminator to guide the training of the autoencoder and the Transformer in an adversarial process. Finally, complex distributions of multivariate time series data can be modeled by the non-linear decoder of the autoencoder. The effectiveness of TimeLAR is empirically underpinned by extensive experiments conducted on five real-world high-dimensional time series datasets in the fields of transportation, electricity, and web page views.

Joint Structural Break Detection and Parameter Estimation in High-Dimensional Non-Stationary VAR Models

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to assume piecewise stationarity, where the model can change at potentially many change points. We propose a three-stage procedure for simultaneous estimation of change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and solve it using a penalized least square estimator with a total variation penalty. We show that the penalized estimation method over-estimates the number of change points, and propose a selection criterion to identify the change points. In the last step of our procedure, we estimate the VAR parameters in each of the segments. We prove that the proposed procedure consistently detects the number and location of change points, and provides consistent estimates of VAR parameters. The performance of the method is illustrated through several simulated and real data examples.