Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes |
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Institution: | 1. School of Mathematics, Honghe University, Yunnan, China;2. School of Mathematics, The University of Manchester, UK;1. CREATES and Department of Economics and Business Economics, Aarhus University, Fuglesangs Allé 4, Building 2628, 8210 Aarhus V, Denmark;2. Department of Economics, Universidad Carlos III de Madrid, Calle Madrid, 126, 28903 Getafe (Madrid), Spain;1. University of Pavia, Italy;2. Cass Business School, City University London, United Kingdom |
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Abstract: | This paper considers methods of deriving sufficient conditions for the central limit theorem and functional central limit theorem to hold in a broad class of time series processes, including nonlinear processes and semiparametric linear processes. The common thread linking these results is the concept of near-epoch dependence on a mixing process, since powerful limit results are available under this limited-dependence property. The particular case of near-epoch dependence on an independent process provides a convenient framework for dealing with a range of nonlinear cases, including the bilinear, GARCH, and threshold autoregressive models. It is shown in particular that even SETAR processes with a unit root regime have short memory, under the right conditions. A simulation approach is also demonstrated, applicable to cases that are analytically intractable. A new FCLT is given for semiparametric linear processes, where the forcing processes are of the NED-on-mixing type, under conditions that are evidently close to necessary. |
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