Inference of time-varying regression models

TL;DR

This paper develops methods for estimating, testing, and selecting variables in models with coefficients that change over time, accommodating complex error structures and providing consistent predictor selection.

Contribution

It introduces a two-stage estimation approach with $n^{1/2}$-convergence, a simulation-based hypothesis test, and an information criterion for variable selection in time-varying coefficient models.

Findings

Parametric component estimated with $n^{1/2}$-rate

Hypothesis testing procedure effectively detects significance

Information criterion accurately identifies true predictors

Abstract

We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a $n^{1/2}$-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion that can consistently select the true set of significant predictors. Our method is applied to autoregressive models with time-varying coefficients. Simulation results and a real data application are provided.