Zihan Wang, Xinghao Qiao, Dong Li, Howell Tong
arXiv 11 Mar 2025 · Statistics — Methodology
arXiv:2503.08655 · PDF · DOI · OpenAlex · Extracted main text
In this article, we propose a novel logistic quasi-maximum likelihood estimation (LQMLE) for general parametric time series models. Compared to the classical Gaussian QMLE and existing robust estimations, it enjoys many distinctive advantages, such as robustness in respect of distributional misspecification and heavy-tailedness of the innovation, more resiliency to outliers, smoothness and strict concavity of the log logistic quasi-likelihood function, and boundedness of the influence function among others. Under some mild conditions, we establish the strong consistency and asymptotic normality of the LQMLE. Moreover, we propose a new and vital parameter identifiability condition to ensure desirable asymptotics of the LQMLE. Further, based on the LQMLE, we consider the Wald test and the Lagrange multiplier test for the unknown parameters, and derive the limiting distributions of the corresponding test statistics. The applicability of our methodology is demonstrated by several time series models, including DAR, GARCH, ARMA-GARCH, DTARMACH, and EXPAR. Numerical simulation studies are carried out to assess the finite-sample performance of our methodology, and an empirical example is analyzed to illustrate its usefulness.
appendix boundary found by appendix_titled_section at “Supplementary Materials” · 100% of the source is main text. Read the extracted text to check this.
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 | Ling \ McAleer (2003) Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory 19(2): 280–310 | 0.843 | 3 | 3 | 100% |
| 2 | Ling \ McAleer (2010) A general asymptotic theory for time-series models, Statistica Neerlandica 64(1): 97–111 | 0.811 | 4 | 2 | 100% |
| 3 | Francq \ Zakoän (2019) GARCH Models: Structure, Statistical Inference and Financial Applications, second edn, John Wiley & Sons | 0.737 | 3 | 2 | 100% |
| 4 | Francq \ Zakoän (2015) Risk-parameter estimation in volatility models, Journal of Econometrics 184(1): 158–173 | 0.644 | 4 | 1 | 100% |
| 5 | Li, Tao, Yang \ Zhang (2023) Maximum likelihood estimation for $$-stable double autoregressive models, Journal of Econometrics 236(1): 105471 | 0.644 | 2 | 2 | 100% |
| 6 | Ling \ Li (1997) On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, Journal of the… | 0.644 | 2 | 2 | 100% |
| 7 | Brockwell \ Davis (1991) Time Series: Theory and Methods, second edn, Springer-Verlag, New York | 0.511 | 2 | 1 | 100% |
| 8 | Huber (1981) Robust Statistics, John Wiley & Sons, Inc., New York | 0.511 | 2 | 1 | 100% |
| 9 | Bardet \ Wintenberger (2009) Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes, The Annals of Statistics 3… | 0.511 | 2 | 1 | 100% |
| 10 | Box, Jenkins, Reinsel \ Ljung (2016) Time Series Analysis: Forecasting and Control, fifth edn, John Wiley & Sons | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 65 scored citations.