Asymptotic Theory for Near Integrated Process Driven by Tempered Linear Process

Farzad Sabzikar, Qiying Wang and Peter Phillips
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Farzad Sabzikar: Dept. of Statistics, Iowa State University
Qiying Wang: University of Sydney

No 2131, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper develops an asymptotic theory for near-integrated random processes and some associated regressions when the errors are tempered linear processes. Tempered processes are stationary time series that have a semi-long memory property in the sense that the autocovariogram of the process resembles that of a long memory model for moderate lags but eventually diminishes exponentially fast according to the presence of a decay factor governed by a tempering parameter. When the tempering parameter is sample size dependent, the resulting class of processes admits a wide range of behavior that includes both long memory, semi-long memory, and short memory processes. The paper develops asymptotic theory for such processes and associated regression statistics thereby extending earlier findings that fall within certain subclasses of processes involving near-integrated time series. The limit results relate to tempered fractional processes that include tempered fractional Brownian motion and tempered fractional diffusions. The theory is extended to provide the limiting distribution for autoregressions with such tempered near-integrated time series, thereby enabling analysis of the limit properties of statistics of particular interest in econometrics, such as unit root tests, under more general conditions than existing theory. Some extensions of the theory to the multivariate case are reported.

Keywords: Asymptotics; Fractional Brownian motion; Long memory; Near Integration; Tempered processes (search for similar items in EconPapers)
JEL-codes: C22 C23 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2018-05
New Economics Papers: this item is included in nep-ecm and nep-ets
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Published in Journal of Econometrics, (May 2020), 216(1): 192-202

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