Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T18:32:36.143Z Has data issue: false hasContentIssue false
  • English
  • Français

LINEAR NONSTATIONARY MODELS—A REVIEW OF THE WORK OF PROFESSOR P.C.B. PHILLIPS

Published online by Cambridge University Press:  10 March 2014

Katsuto Tanaka
Katsuto Tanaka*
Affiliation:
Hitotsubashi University
*
*Address correspondence to Katsuto Tanaka, Department of Economics Hitotsubashi University Kunitachi, Tokyo 186-8601 Japan; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

The work of Professor P.C.B. Phillips, even if it is focused on the area of linear nonstationary models, is enormous. So it is hard for me to explore the whole of his work in this paper. Therefore, I have decided to take up only a few results of his work. The topics chosen here are applications of the martingale approximation and the problem of choosing between stochastic and deterministic trends, which I discuss and, hopefully, extend.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 4 , August 2014 , pp. 815 - 838
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahtola, J. & Tiao, G.C. (1987) Distributions of least squares estimators of autoregressive parameters for a process with complex roots on the unit circle. Journal of Time Series Analysis 8, 1–14.CrossRefGoogle Scholar
Anderson, T.W. (1971) The Statistical Analysis of Time Series. Wiley.Google Scholar
Beveridge, S. & Nelson, C.R. (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the ‘business cysle’. Journal of Monetary Economics 7, 151–174.Google Scholar
Bierens, H.J. (2001) Complex unit roots and business cycles: Are they real? Econometric Theory 17, 962–983.Google Scholar
Chan, N.H. & Wei, C.Z. (1988) Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of Statistics 16, 367–401.Google Scholar
Csörgő, K & Horváth, L. (1993) Weighted Approximations in Probability and Statistics. Wiley.Google Scholar
Gordin, M.I. (1969) The central limit theorem for stationary processes. Soviet Mathematics Doklady 10, 1174–1176.Google Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Application. Academic Press.Google Scholar
Helland, I.S. (1982) Central limit theorems for martingales with discrete or continuous time. Scandinavian Journal of Statistics 9, 79–94.Google Scholar
Hochstadt, H. (1973) Integral Equations. Wiley.Google Scholar
Loève, M. (1978) Probability Theory II, 4th ed.Springer-Verlag.CrossRefGoogle Scholar
Nabeya, S. (2001) Unit root seasonal autoregressive models with a polynomial trend of higher degree. Econometric Theory 17, 357–385.CrossRefGoogle Scholar
Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277–301.Google Scholar
Phillips, P.C.B. (1988) Weak convergence of sample covariance matrices to stochastic integrals via martingale approximations. Econometric Theory 4, 528–533.CrossRefGoogle Scholar
Phillips, P.C.B. (1998) New tools for understanding spurious regressions. Econometrica 66, 1299–1325.Google Scholar
Phillips, P.C.B. (1999) Discrete Fourier transforms of fractional processes. Cowles Foundation Discussion Paper 1243.Google Scholar
Phillips, P.C.B. (2002) New unit root asymptotics in the presence of deterministic trends. Journal of Econometrics 111, 323–353.Google Scholar
Phillips, P.C.B. (2005) HAC estimation by automated regression. Econometric Theory 21, 116–142.CrossRefGoogle Scholar
Phillips, P.C.B. (2006) Optimal estimation of cointegrated systems with irrelevant instruments. Cowles Foundation Discussion Paper 1547.Google Scholar
Phillips, P.C.B. & Solo, V. (1992). Asymptotics for linear processes. Annals of Statistics 20, 971–1001.Google Scholar
Said, E.S. & Dickey, D.A. (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71, 599–607.Google Scholar
Tanaka, K. (1996) Time Series Analysis: Nonstationary and Noninvertible Distribution Theory. Wiley.Google Scholar
Tanaka, K. (2001) K -asymptotics associated with deterministic trends in the integrated and near-integrated processes. The Japanese Economic Review 52, 35–63.Google Scholar
Tanaka, K. (2008) Analysis of models with complex roots on the unit circle. Journal of the Japan Statistical Society 38, 145–155.Google Scholar