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Asymptotic theory for near integrated processes driven by tempered linear processes

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 accordingto 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 secondkind. 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 arereported.
0304-4076
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
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 (2019) Asymptotic theory for near integrated processes driven by tempered linear processes. Journal of Econometrics. (In Press)

Record type: Article

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 accordingto 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 secondkind. 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 arereported.

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Accepted/In Press date: 10 September 2019

Identifiers

Local EPrints ID: 435267
URI: https://eprints.soton.ac.uk/id/eprint/435267
ISSN: 0304-4076
PURE UUID: 7727d9c8-d854-40a5-8efe-6ba46d9feada
ORCID for Peter Charles Bonest Phillips: ORCID iD orcid.org/0000-0003-2341-0451

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Date deposited: 29 Oct 2019 17:30
Last modified: 30 Oct 2019 01:34

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