Simultaneous Inference of a Partially Linear Model in Time Series

TL;DR

This paper develops a new methodology for simultaneous inference of multivariate nonparametric functions in partially linear time series models, accommodating complex dependence structures and providing practical confidence regions.

Contribution

It introduces a novel approach extending Gaussian approximation to dependent processes for constructing simultaneous confidence regions in multivariate nonparametric time series models.

Findings

Method effectively handles complex dependence structures.

Simulation studies confirm finite-sample validity.

Application demonstrates practical utility in financial data analysis.

Abstract

We introduce a new methodology to conduct simultaneous inference of the nonparametric component in partially linear time series regression models where the nonparametric part is a multivariate unknown function. In particular, we construct a simultaneous confidence region (SCR) for the multivariate function by extending the high-dimensional Gaussian approximation to dependent processes with continuous index sets. Our results allow for a more general dependence structure compared to previous works and are widely applicable to a variety of linear and nonlinear autoregressive processes. We demonstrate the validity of our proposed methodology by examining the finite-sample performance in the simulation study. Finally, an application in time series, the forward premium regression, is presented, where we construct the SCR for the foreign exchange risk premium from the exchange rate and macroeconomic data.