北京雁栖湖应用数学研究院

韩立岩 , 李振 , 刘庆富 , 龙飞 , 汤珂

Jiajing Su

2024年12月09日 15:20 至 16:20

A3-2-303

Zoom 230 432 7880 (BIMSA)

The self-normalization (SN) approach proposed by Lobato (2001) and Shao (2010) is based on the variance of the partial sum of a time series process, which is sensitive to irregularities such as persistent autocorrelation, heteroskedasticity, near-unit roots, and outliers. The existing self-normalized approach to inference for time series was first introduced by Shao (2010) as a generalization of an idea devised and developed by Kiefer et al. (2000) and Lobato (2001). Since its introduction, SN has been deployed in various aspects of statistical inference, such as confidence interval construction (Shao, 2010), testing for autocorrelation (Lobato, 2001; Shao, 2010; Boubacar-Maïnassara and Saussereau, 2018), testing for structural breaks (Shao and Zhang, 2010; Zhang et al., 2011; Zhang and Lavitas, 2018), and has been applied to various types of data, such as functional time series (Zhang et al., 2011; Dette et al., 2020), spatial data (Zhang et al., 2014), censored dependent data (Huang et al., 2015), and alternating regime index datasets (Kim and Shin, 2020). SN has also been applied across many academic fields of study, including economics (Lobato, 2001; Shao, 2010), finance (Choi and Shin, 2021, 2020), ecology (Zhang et al., 2014), climate studies (Dette et al., 2020), and epidemiology (Jiang et al., 2023). This paper introduces a novel approach to confidence interval construction and hypothesis testing for time series analysis, using the adjusted-range-based self-normalization proposed by Hong et al. (2024). Similar to Shao’s (2010) method, the adjusted-range-based self-normalizer is an inconsistent long-run variance (covariance) estimator but is stochastically proportional to the actual long-run variance (covariance), yielding pivotal statistics and circumventing the need for parameter specifications such as bandwidth, kernel, or block size in block bootstrap methods. The paper focuses on the construction of confidence intervals and hypothesis testing for a class of statistical quantities expressible as functionals of empirical distributions. This class includes the approximately linear statistics described in Shao (2010), encompassing mean, variance, quantiles, and others, as well as estimated coefficients in general regression models, such as M-estimators, maximum likelihood (ML) estimators, and least squares (LS) estimators. Through extensive simulation and empirical studies, the effectiveness of the adjusted-range-based self-normalization approach is demonstrated. In particular, it offers a more balanced size-power trade-off and generates significantly narrower confidence intervals compared to Shao’s (2010) self-normalization method.

Dr. Jiajing Sun is an Associate Professor at the School of Economics and Management (SEM), University of Chinese Academy of Sciences (UCAS), a Chartered Financial Analyst, and the Deputy Director of the Department of Statistics and Data Science at SEM-UCAS. Her main research areas include econometrics, statistics, and finance. Dr. Sun has published several papers in internationally recognized journals such as the Journal of Econometrics, Journal of the Royal Statistical Society: Series B, Economics Letters, Journal of Time Series Analysis, Journal of Environmental Management, Journal of Multivariate Analysis, and Energy Economics.