Confidence bands in nonparametric time series regression

TL;DR

This paper develops methods for constructing asymptotically correct confidence bands for mean and variance functions in nonlinear time series models, with applications to financial data like the S&P 500 Index.

Contribution

It introduces a framework for simultaneous confidence bands in nonparametric time series regression accommodating complex dependence structures.

Findings

Confidence bands have asymptotically correct coverage probabilities.

Applicable to a wide range of linear and nonlinear autoregressive processes.

Demonstrated on S&P 500 Index data.

Abstract

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear auto-regressive processes. The results are applied to the S&P 500 Index data.