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ESTIMATION AND INFERENCE WITH NEAR UNIT ROOTS
Open accessAbstract
New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local unit-root (LUR), mildly integrated (MI), and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME specifications and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade.
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GDP, FD, and INV are stationary at first difference, while OIL and INF are stationary at level.
“The result of unit root shows that GDP, FD and INV are stationary at first difference, however, OIL and INF are stationary at level, so the result of the unit root test gives the level of confidence for the application of panel ARDL for estimation [51,52,53,54].”
From Dynamics of economic growth in ASEAN-5 countries: a panel ARDL approach (2024) · cites this paper as [51]
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Testing the null hypothesis of stationarity against the alternative of a unit root
Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992) · Journal of Econometrics · doi:10.1016/0304-4076(92)90104-y · Cited by 12,633
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Phillips, P. C. B. (1987) · Econometrica · doi:10.2307/1913237 · Cited by 2,821
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Shorack, G. R., & Wellner, J. A. (2009) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719017 · Cited by 2,310
On the probable error of a coefficient of correlation deduced from a small sample
Fisher, R. A. (1921) · Adelaide Research & Scholarship (AR&S) (University of Adelaide) · Cited by 2,089
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Keener, R. W. (2009) · Springer texts in statistics · doi:10.1007/978-0-387-93839-4_1 · Cited by 302
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Elliott, G. (1998) · Econometrica · doi:10.2307/2998544 · Cited by 243
Phillips, P. C. B. (1977) · Econometrica · doi:10.2307/1911222 · Cited by 208
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Satchell, S. (1984) · Econometrica · doi:10.2307/1910999 · Cited by 38
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Winterbottom, A. (1979) · The American Statistician · doi:10.1080/00031305.1979.10482682 · Cited by 38
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Metadata
- Authors
- Phillips, P. C. B.
- Affiliations
- University of Auckland (NZ)
- Corresponding author
- Phillips, Peter C.B.
- ORCID
- Phillips, Peter C.B.
- Venue
- Econometric Theory
- Publisher
- Cambridge University Press (CUP)
- Published
- 2022-07-27
- Volume
- 39
- Issue
- 2
- Pages
- 221-263
- ISSN
- 0266-4666 (ISSN-L)
- 1469-4360
- OpenAlex
- W3210210310
- Cited by
- 44
- References
- 39
- Citations by year
- 2026: 9 · 2025: 23 · 2024: 3 · 2023: 6 · 2022: 3
- FWCI
- 12.10
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Econometric Theory (publishedVersion, cc-by)
- ePrints Soton (University of Southampton) (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Singapore Management University Institutional Knowledge (InK) (Singapore Management University) (submittedVersion, cc-by)
- Funders
- National Science Foundation (0956687, 1850860)
- University of Auckland
- Topics
- Social Sciences › Economics, Econometrics and Finance › General Economics, Econometrics and Finance › Monetary Policy and Economic Impact
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Diverse Scientific and Economic Studies
- Physical Sciences › Computer Science › Signal Processing › Time Series Analysis and Forecasting
- Keywords
- near unit root, non-stationary time series, asymptotic distribution, variance stabilization, housing prices, housing market
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