Functional coefficient autoregressive models for vector time series |
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| Affiliation: | 1. Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi, 39762-9715, USA;2. Department of Mathematical Sciences, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA;1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, PR China;2. CSIRO Digital Productivity Flagship, Private Bag 5, Wembley, WA 6913, Australia;3. Department of Applied Mathematics, the Hong Kong Polytechnic University, Hong Kong;4. Institute of Statistical Science, Shenzhen University, Shenzhen 518060, China;1. London School of Economics and Political Science, Department of Statistics, United Kingdom;2. Universitat Pompeu Fabra, Department of Economics and Business & Barcelona GSE, Spain;3. Università di Firenze, Dipartimento di Statistica, Informatica, Applicazioni, Italy;4. ECARES, Solvay Brussels School of Economics and Management, Université libre de Bruxelles, Belgium;5. Institute of Economic Studies, Charles University, Opletalova 21, 110 00, Prague, Czech Republic;1. Bocconi University, IGIER, Italy;2. CEPR, United Kingdom;3. European University Institute, Italy;4. Bank of Slovenia, Slovenia;1. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China;2. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China;3. School of Statistics, Renmin University of China, Beijing, China;4. Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA |
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| Abstract: | We extend the functional coefficient autoregressive (FCAR) model to the multivariate nonlinear time series framework. We show how to estimate parameters of the model using kernel regression techniques, discuss properties of the estimators, and provide a bootstrap test for determining the presence of nonlinearity in a vector time series. The power of the test is examined through extensive simulations. For illustration, we apply the methods to a series of annual temperatures and tree ring widths. Computational issues are also briefly discussed. |
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