Lujia Bai, Weichi Wu
arXiv 15 Oct 2021 · Mathematics — Statistics Theory · publishedBernoulli (2024) · 1 citations (OpenAlex)
arXiv:2110.08089 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Wu, W. and Zhou, Z (2018) Simultaneous quantile inference for non-stationary long-memory time series self | 1.000 | 5 | 3 | 100% |
| 2 | Wu, W. and Zhou, Z (2018) Gradient-based structural change detection for nonstationary time series M-estimation self | 0.843 | 4 | 3 | 75% |
| 3 | Dette, H., Preuss, P., and Sen, K (2017) Detecting long-range dependence in non-stationary time series | 0.843 | 3 | 3 | 100% |
| 4 | Ferreira, G., Piña, N., and Porcu, E (2018) Estimation of slowly time-varying trend function in long memory regression models | 0.843 | 3 | 3 | 100% |
| 5 | Wu, W. B. and Shao, X (2006) Invariance principles for fractionally integrated nonlinear processes self | 0.843 | 3 | 3 | 100% |
| 6 | Zhou, Z. and Wu, W. B (2010) Simultaneous inference of linear models with time varying coefficients self | 0.838 | 17 | 6 | 59% |
| 7 | Fan, J. and Zhang, W (2000) Simultaneous confidence bands and hypothesis testing in varying-coefficient models | 0.811 | 4 | 2 | 100% |
| 8 | Wu, W. B. and Zhou, Z (2011) Gaussian approximations for non-stationary multiple time series self | 0.737 | 4 | 3 | 50% |
| 9 | Beran, J., Feng, Y., Ghosh, S., and Kulik, R (2013) Long-Memory Processes | 0.644 | 3 | 2 | 67% |
| 10 | Dette, H. and Wu, W (2019) Detecting relevant changes in the mean of nonstationary processes—a mass excess approach self | 0.644 | 3 | 2 | 67% |
Showing the top 10 of 65 scored citations.