Sequential Quantile Prediction of Time Series

TL;DR

This paper introduces a sequential nonparametric quantile prediction model for real-valued time series, combining expert predictors and demonstrating consistency and superior performance on real data.

Contribution

It proposes a novel sequential quantile forecasting approach based on expert aggregation, with proven consistency and improved accuracy over standard methods.

Findings

Model outperforms standard quantile prediction methods on real data

Demonstrates consistency under minimal conditions

Effective nonparametric strategy for time series quantile prediction

Abstract

Motivated by a broad range of potential applications, we address the quantile prediction problem of real-valued time series. We present a sequential quantile forecasting model based on the combination of a set of elementary nearest neighbor-type predictors called "experts" and show its consistency under a minimum of conditions. Our approach builds on the methodology developed in recent years for prediction of individual sequences and exploits the quantile structure as a minimizer of the so-called pinball loss function. We perform an in-depth analysis of real-world data sets and show that this nonparametric strategy generally outperforms standard quantile prediction methods