Simultaneous nonparametric inference of time series

TL;DR

This paper develops a method for simultaneous nonparametric inference of time series, providing asymptotic Gumbel distributions for kernel estimates, enabling confidence bands and goodness-of-fit tests for complex models.

Contribution

It generalizes existing results to a broad class of stationary processes, allowing for simultaneous inference on densities and regression functions in time series.

Findings

Asymptotic Gumbel distribution for kernel estimates

Construction of simultaneous confidence bands for densities and regression functions

Application to yield curve rate modeling

Abstract

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and regression estimates are asymptotically Gumbel. Our results substantially generalize earlier ones which were obtained under independence or beta mixing assumptions. The asymptotic results can be applied to assess patterns of marginal densities or regression functions via the construction of simultaneous confidence bands for which one can perform goodness-of-fit tests. As an application, we construct simultaneous confidence bands for drift and volatility functions in a dynamic short-term rate model for the U.S. Treasury yield curve rates data.