# Spline Single-Index Prediction Model

## TL;DR

This paper introduces a robust single-index prediction model using spline estimators, effective for high-dimensional, weakly dependent data, with proven consistency, normality, and fast computation, demonstrated through simulations and real data application.

## Contribution

It proposes a spline-based single-index prediction method that is robust, computationally efficient, and applicable to high-dimensional, dependent data, extending existing models.

## Key findings

- Spline estimator is root-n consistent and asymptotically normal.
- The iterative routine is fast enough for large, high-dimensional data.
- Application to Icelandic river flow data shows superior forecasting performance.

## Abstract

For the past two decades, single-index model, a special case of projection pursuit regression, has proven to be an efficient way of coping with the high dimensional problem in nonparametric regression. In this paper, based on weakly dependent sample, we investigate the single-index prediction (SIP) model which is robust against deviation from the single-index model. The single-index is identified by the best approximation to the multivariate prediction function of the response variable, regardless of whether the prediction function is a genuine single-index function. A polynomial spline estimator is proposed for the single-index prediction coefficients, and is shown to be root-n consistent and asymptotically normal. An iterative optimization routine is used which is sufficiently fast for the user to analyze large data of high dimension within seconds. Simulation experiments have provided strong evidence that corroborates with the asymptotic theory. Application of the proposed procedure to the rive flow data of Iceland has yielded superior out-of-sample rolling forecasts.