Properties of nonlinear transformations of fractionally integrated processes |
| |
| Authors: | Ingolf Dittmann Clive W J Granger |
| |
| Institution: | 1. School of Business and Economics, Humboldt University, Berlin, 10178 Berlin, Germany;2. Department of Economics, University of California, San Diego, La Jolla, CA 92093-0508, USA;1. Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China;2. School of Science, Beijing Jiaotong University, Beijing 100044, China;1. Department of Economics, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV, 89557, USA;2. Department of Economics, Michigan State University, East Lansing, MI, USA;1. Department of Neurosurgery, Shengjing Hospital of China Medical University, Shenyang 110004, People''s Republic of China;2. Department of Neurobiology, College of Basic Medicine, China Medical University, Shenyang 110001, People''s Republic of China;3. Institute of Pathology and Pathophysiology, China Medical University, Shenyang 110001, People''s Republic of China;1. Kazakh-British Technical University, Almaty 050000, Kazakhstan;2. School of Mathematics, University of Manchester, Manchester M13 9PL, UK;3. Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand;4. Kazakh National University, Almaty, Kazakhstan;1. Department of Neurological Surgery, Dardinger Laboratory for Neuro-Oncology and Neurosciences, The Ohio State University Comprehensive Cancer Center and Wexner Medical Center, Columbus, Ohio, USA;2. Department of Otolaryngology-Head and Neck Surgery, The James Cancer Hospital and Solove Research Institute, Wexner Medical Center at The Ohio State University, Columbus, Ohio, USA;3. Center for Biostatistics, Department of Biomedical Informatics, The Ohio State University, Columbus, Ohio, USA;4. Chemistry of Life Processes Institute and Robert H. Lurie Comprehensive Cancer Center, Northwestern University, Evanston, Illinois, USA;1. Economic and Financial Statistics Unit, Department of Statistics, University of Ibadan, Nigeria;2. Department of Economics, Faculty of Economics and Administration, University of Malaya, Malaysia;3. Asia–Europe Institute, University of Malaya, Malaysia;4. Faculty of Law, University of Malaya, Malaysia;5. Africa-Asia Development University Network, University of Malaya, Malaysia |
| |
| Abstract: | This paper shows that the properties of nonlinear transformations of a fractionally integrated process strongly depend on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d>0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0)). For non-stationary I(d) processes, every polynomial transformation is non-stationary and exhibits a stochastic trend in mean and in variance. In particular, the square of a non-stationary Gaussian I(d) process still has long memory with parameter d, whereas the square of a stationary Gaussian I(d) process shows less dependence than the initial process. Simulation results for other transformations are also discussed. |
| |
| Keywords: | Long memory Nonlinearity Non-stationarity Fractional integration |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
