Detecting long-range dependence for time-varying linear models

TL;DR

This paper develops and analyzes bootstrap-assisted tests for detecting long-range dependence in time-varying linear models with complex dynamics, heteroscedasticity, and covariates, providing theoretical and empirical validation.

Contribution

It introduces new bootstrap-based tests for long-range dependence in non-stationary models, with proven consistency and comparable power to classical tests in stationary cases.

Findings

Tests are consistent under degenerate and non-degenerate scenarios.

Bootstrap-assisted tests achieve the same local asymptotic power as classical KPSS.

Extensive simulations and real data analysis validate the methods.

Abstract

We consider the problem of testing for long-range dependence in time-varying coefficient regression models, where the covariates and errors are locally stationary, allowing complex temporal dynamics and heteroscedasticity. We develop KPSS, R/S, V/S, and K/S-type statistics based on the nonparametric residuals. Under the null hypothesis, the local alternatives as well as the fixed alternatives, we derive the limiting distributions of the test statistics. As the four types of test statistics could degenerate when the time-varying mean, variance, long-run variance of errors, covariates, and the intercept lie in certain hyperplanes, we show the bootstrap-assisted tests are consistent under both degenerate and non-degenerate scenarios. In particular, in the presence of covariates the exact local asymptotic power of the bootstrap-assisted tests can enjoy the same order as that of the classical KPSS test of long memory for strictly stationary series. The asymptotic theory is built on a new Gaussian approximation technique for locally stationary long-memory processes with short-memory covariates, which is of independent interest. The effectiveness of our tests is demonstrated by extensive simulation studies and real data analysis.