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Linear autoregressive models serve as basic representations of discrete timestochastic processes. Different attempts have been made to provide non-linearversions of the basic autoregressive process, including different versionsbased on kernel methods. Motivated by the powerful framework of Hilbert spaceembeddings of distributions, in this paper we apply this methodology for thekernel embedding of an autoregressive process of order $p$. By doing so, weprovide a non-linear version of an autoregressive process, that shows increasedperformance over the linear model in highly complex time series. We use themethod proposed for one-step ahead forecasting of different time-series, andcompare its performance against other non-linear methods.

Short-term time series prediction using Hilbert space embeddings of autoregressive processes