Asymptotic theory for near integrated processes driven by tempered linear processes
Asymptotic theory for near integrated processes driven by tempered linear processes
In an early article on near-unit root autoregression, Ahtola and Tiao (1984) studied the behavior of the score function in a stationary first order autoregression driven by independent Gaussian innovations as the autoregressive coefficient approached unity from below. The present paper develops asymptotic theory for near-integrated random processes and associated regressions including the score function in more general settings where 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 of the second kind. 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.
Asymptotics, Fractional integration, Integrated process, Near unit root, Tempered process
192-202
Sabzikar, Farzad
57eae0d2-414f-4cdf-8760-c0f12b60af03
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Qiying
c9b51dcb-4b59-4177-839a-c6b5fff6e991
May 2020
Sabzikar, Farzad
57eae0d2-414f-4cdf-8760-c0f12b60af03
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Wang, Qiying
c9b51dcb-4b59-4177-839a-c6b5fff6e991
Sabzikar, Farzad, Phillips, Peter Charles Bonest and Wang, Qiying
(2020)
Asymptotic theory for near integrated processes driven by tempered linear processes.
Journal of Econometrics, 216 (1), .
(doi:10.1016/j.jeconom.2020.01.013).
Abstract
In an early article on near-unit root autoregression, Ahtola and Tiao (1984) studied the behavior of the score function in a stationary first order autoregression driven by independent Gaussian innovations as the autoregressive coefficient approached unity from below. The present paper develops asymptotic theory for near-integrated random processes and associated regressions including the score function in more general settings where 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 of the second kind. 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.
Text
Revised-10-09-19-Main_text-pcb
- Accepted Manuscript
More information
Accepted/In Press date: 10 September 2019
e-pub ahead of print date: 31 January 2020
Published date: May 2020
Additional Information:
Funding Information:
The authors thank the co-editor and two referees for their very helpful comments on the original version and revision of this paper. Phillips acknowledges research support from the Kelly Fund at the University of Auckland and the National Science Foundation under Grant No. SES 18-50860. Wang acknowledges research support from the Australian Research Council under grant No. DP170104385.
Publisher Copyright:
© 2020 Elsevier B.V.
Keywords:
Asymptotics, Fractional integration, Integrated process, Near unit root, Tempered process
Identifiers
Local EPrints ID: 435267
URI: http://eprints.soton.ac.uk/id/eprint/435267
ISSN: 0304-4076
PURE UUID: 7727d9c8-d854-40a5-8efe-6ba46d9feada
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Date deposited: 29 Oct 2019 17:30
Last modified: 16 Mar 2024 08:19
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Author:
Farzad Sabzikar
Author:
Qiying Wang
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