Structure of the third moment of the generalized Rosenblatt distribution |
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| Institution: | 1. Mathematical Sciences Center and Tsinghua Center for Statistics Science, Tsinghua University, Beijing 100084, China;2. School of Economics and Wang Yanan Institute for Studies in Economics (WISE), Xiamen University, Xiamen 361005, China;3. School of Business, Renmin University of China, Beijing 100084, China;1. Afdeling Statistiek, Celestijnenlaan 200b - bus 2400, 3001 Leuven, Belgium;2. Faculty of Business and Economics, ORSTAT, KU Leuven, Belgium;1. University of Pittsburgh, United States;2. University of Haifa, Israel |
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| Abstract: | The Rosenblatt distribution appears as limit in non-central limit theorems. The generalized Rosenblatt distribution is obtained by allowing different power exponents in the kernel that defines the usual Rosenblatt distribution. We derive an explicit formula for its third moment, correcting the one in Maejima and Tudor (2012) and Tudor (2013). Evaluating this formula numerically, we are able to confirm that the class of generalized Hermite processes is strictly richer than the class of Hermite processes. |
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| Keywords: | Long memory Self-similar processes Rosenblatt processes Generalized Rosenblatt processes |
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