Online Learning for Time Series Prediction

TL;DR

This paper introduces online learning algorithms for time series prediction using ARMA models that do not rely on traditional noise assumptions, achieving performance close to the best possible ARMA model in hindsight.

Contribution

It presents novel online algorithms for ARMA-based time series prediction that work under minimal noise assumptions, with proven asymptotic optimality.

Findings

Algorithms perform close to the best ARMA model in hindsight

Effective in non-Gaussian, dependent noise settings

Asymptotic regret bounds established

Abstract

In this paper we address the problem of predicting a time series using the ARMA (autoregressive moving average) model, under minimal assumptions on the noise terms. Using regret minimization techniques, we develop effective online learning algorithms for the prediction problem, without assuming that the noise terms are Gaussian, identically distributed or even independent. Furthermore, we show that our algorithm's performances asymptotically approaches the performance of the best ARMA model in hindsight.