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In this paper, we consider high-dimensional stationary processes where a new observation is generated from a compressed version of past observations. The specific evolution is modeled by an encoder-decoder structure. We estimate the evolution with an encoder-decoder neural network and give upper bounds for the expected forecast error under specific structural and sparsity assumptions. The results are shown separately for conditions either on the absolutely regular mixing coefficients or the functional dependence measure of the observed process. In a quantitative simulation we discuss the behavior of the network estimator under different model assumptions. We corroborate our theory by a real data example where we consider forecasting temperature data.
We provide statistical theory for conditional and unconditional Wasserstein generative adversarial networks (WGANs) in the framework of dependent observations. We prove upper bounds for the excess Bayes risk of the WGAN estimators with respect to a m
Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables de
We present a method for conditional time series forecasting based on an adaptation of the recent deep convolutional WaveNet architecture. The proposed network contains stacks of dilated convolutions that allow it to access a broad range of history wh
Cyber-physical systems often consist of entities that interact with each other over time. Meanwhile, as part of the continued digitization of industrial processes, various sensor technologies are deployed that enable us to record time-varying attribu
With the rising number of interconnected devices and sensors, modeling distributed sensor networks is of increasing interest. Recurrent neural networks (RNN) are considered particularly well suited for modeling sensory and streaming data. When predic