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

TL;DR

This paper introduces a non-linear autoregressive model using Hilbert space embeddings, demonstrating improved forecasting performance on complex time series compared to traditional linear models.

Contribution

It applies Hilbert space embeddings to create a non-linear autoregressive process, enhancing prediction accuracy for complex time series.

Findings

Outperforms linear autoregressive models on complex data

Shows increased forecasting accuracy over other non-linear methods

Effective for one-step ahead time series prediction

Abstract

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.