Yuxin Tao, Feiyu Jiang, Xiaofeng Shao
arXiv 28 May 2026 · Econometrics
arXiv:2605.29315 · PDF · DOI · OpenAlex · Extracted main text
Residual-based goodness-of-fit tests for parametric time-series models are often complicated by parameter-estimation effects, which can alter the limiting behavior of diagnostic statistics. We propose a sample-splitting generalized spectral test (in the spirit of Escanciano(2006)) for assessing conditional mean specification in linear and nonlinear time-series models. The procedure estimates the model parameter on a fitting subsample and constructs a generalized spectral Cramer-von Mises statistic from residuals computed on a checking/testing subsample. The statistic aggregates pairwise conditional mean restrictions over all lags and is therefore bandwidth-free and free of truncation-lag selection. Under mild regularity conditions and a score-alignment condition, the residual-based process has the same limiting null distribution as the infeasible oracle process based on the true errors. Although the resulting limiting law is still non-pivotal, it can be consistently approximated by a simple multiplier bootstrap that does not require generating bootstrap time series or re-estimating parameters. Such an oracle-equivalence property is in sharp contrast to the original full-sample test, for which parameter estimation contributes an additional first-order term to the limiting process, and requires re-estimating parameters in each bootstrapped sample. We further establish consistency of the proposed test against fixed alternatives and nontrivial power against local alternatives. Extensive simulations and real data analyses show that the proposed test controls size well, has comparable power, and delivers substantial computational savings in models where repeated estimation is costly.
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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 | Escanciano, Juan Carlos (2008) Joint and Marginal Specification Tests for Conditional Mean and Variance Models | 1.000 | 6 | 3 | 100% |
| 2 | Escanciano, J Carlos (2006) Goodness-of-fit tests for linear and nonlinear time series models | 0.961 | 27 | 8 | 89% |
| 3 | Davis, Richard A and Fernandes, Leon (2025) Sample splitting and assessing goodness-of-fit of time series | 0.874 | 6 | 3 | 67% |
| 4 | Escanciano, Juan Carlos (2024) A Gaussian Process Approach to Model Checks | 0.644 | 2 | 2 | 100% |
| 5 | Hong, Yongmiao and Lee, Yoon-Jae (2005) Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroskedasticity of Unknown Form | 0.644 | 2 | 2 | 100% |
| 6 | Wang, Guochang and Zhu, Ke and Shao, Xiaofeng (2022) Testing for the Martingale Difference Hypothesis in Multivariate Time Series Models self | 0.644 | 2 | 2 | 100% |
| hong2005generalized | unmatched citation key hong2005generalized | 0.585 | 3 | 1 | 100% |
| 8 | Tsay, Ruey S (1989) Testing and modeling threshold autoregressive processes | 0.585 | 3 | 1 | 100% |
| 9 | Ling, Shiqing and McAleer, Michael (2003) Asymptotic theory for a vector ARMA-GARCH model | 0.511 | 3 | 2 | 33% |
| 10 | Koul, Hira and Stute, Winfried (1999) Nonparametric Model Checks for Time Series | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 43 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.