Model-free prediction of time series: a nonparametric approach

Abstract

We propose a novel approach for model-free time series forecasting. Unlike most existing methods, the proposed method does not rely on parametric error distributions nor assume parametric forms of the mean function, leading to broad applicability. We achieve such generality by establishing a simple but powerful representation of a time series $\{X_t;t\in \mathbb{Z}\}$ with $\underset{t}{sup}E|X_t|<\mathrm{\infty }$, that is, $X_t$ has a solution which is a linear combination of infinite past values. Then using the obtained solution a prediction algorithm is presented, with large sample theoretical guarantees. Simulation studies show favourable performance of the proposed method compared with popular parametric and neural networks methods, and suggest its superiority when the sample size is small. An application to practical time series is discussed.

Keywords:

• Prediction
• nonparametric methods
• neural networks
• α-stable distribution

MSC2010 subject classifications::

• Primary: 60G25
• Secondary: 62M20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 See https://www.sciencedirect.com/topics/engineering/left-inverse.