Short-term time series prediction using Hilbert space embeddings of autoregressive processes
This work addresses the need for improved forecasting in complex time series, but it appears incremental as it builds on existing kernel and embedding methods.
The authors tackled the problem of short-term time series prediction by developing a non-linear version of autoregressive processes using Hilbert space embeddings, which showed increased performance over linear models in complex time series, though specific numerical gains were not detailed.
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings of distributions, in this paper we apply this methodology for the kernel embedding of an autoregressive process of order $p$. By doing so, we provide a non-linear version of an autoregressive process, that shows increased performance over the linear model in highly complex time series. We use the method proposed for one-step ahead forecasting of different time-series, and compare its performance against other non-linear methods.