Abstract: This paper proposes a generalized bispectrum as a new analytic tool for nonlinear time series. Compared to Hong's (1999) generalized spectral density, the generalized bispectrum can capture nonlinear serial dependences which are pairwise independent but are not triple-wise independent. Furthermore, the conventional bispectrum can be obtained as a special case by taking a third order derivative of the generalized bispectrum at the origin. We propose a nonparametric bi-kernel estimator for the generalized bispectrum and derive its asymptotic integrated mean squared error (IMSE) with convergence rates, thus establishing its consistency property. 
As an application, we use the bi-kernel based bispectral density to construct a squared L2-norm type test for nonlinear serial dependences. We derive the asymptotic normality of the proposed test statistic under the null hypothesis of serial independence. Monte Carlo simulation studies show that the proposed test has reasonable power against a wide range of nonlinear dependent processes and is particularly informative for joint nonlinear dependence. An empirical application to daily exchange-rate returns reveals heterogeneous pairwise and triple-wise dependence patterns across major currencies.

个人简介：洪永淼，中国科学院数学与系统科学研究院关肇直首席研究员，中国科学院大学经济与管理学院院长，发展中国家科学院院士，世界计量经济学会会士，亚太人工智能学会会士，亚洲金融经济研究局高级会士，教育部高等学校经济学类专业教学指导委员会副主任委员。曾任美国康奈尔大学经济学与国际研究讲席教授、统计学教授，中国留美经济学会会长。

研究领域为计量经济学、时间序列分析、金融计量学、统计学，在Annals of Statistics、Biometrika、Econometrica、Journal of American Statistical Association、Journal of Political Economy、Journal of Royal Statistical Society B、Management Science、Quarterly Journal of Economics、Review of Economic Studies、Review of Financial Studies、《经济研究》《管理世界》《中国工业经济》《管理科学学报》《中国科学院院刊》等经济学、金融学和统计学中英文主流期刊发表文章200余篇。出版《Python经济大数据分析》《概率论与统计学》《高级计量经济学》、Probability and Statistics for Economists、Foundations of Modern Econometrics: A Unified Approach等中英文著作。2014-2025年连续12年入选Elsevier经济学/统计学中国高被引学者榜单，获2022年高等教育（本科）国家级教学成果奖一等奖。