Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T21:24:39.045Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation of Cointegrated Systems with I(2) Processes

Published online by Cambridge University Press:  11 February 2009

Yuichi Kitamura
Yuichi Kitamura
Affiliation:
University of Minnesota
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the properties of systems likelihood procedures for cointegrated systems when the I(2) variables are present. Two alternative methods are proposed: one is based on the full system likelihood, whereas another is based on the subsystem likelihood. By eliminating all unit roots in the system by the use of prior information concerning the presence of unit roots, these procedures yield estimates whose asymptotic distributions are mixed normal, free from nuisance parameters, and median-unbiased. Both methods are extensions of a full system maximum likelihood procedure by Phillips (1991a) to I(2) models. Three cases of cointegration with I(2) variables are considered in order to cover a wide variety of cointegration relationships. A triangular ECM representation and the two ML estimates are derived for each case, and the asymptotics are discussed as well. The asymptotic efficiency concerning the two estimates are considered.

Information

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 1 , February 1995 , pp. 1 - 24
Copyright
Copyright © Cambridge University Press 1995

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Ahn, S.K. & Reinsel, G.C. (1988) Nested reduced rank autoregressive models for multiple time series. Journal of the American Statistical Association 83, 849–856.Google Scholar
Ahn, S.K. & Reinsel, G.C. (1990) Estimation for partially nonstationary multivariate autoregressive models. Journal of the American Statistical Association 85, 813–823.CrossRefGoogle Scholar
Basawa, I.V. & Scott, D.J. (1983) Asymptotic Optimal Inference for Non-Ergodic Models. New York: Springer-Verlag.CrossRefGoogle Scholar
Dunsmuir, W. (1979) A central limit theorem for parameter estimation in stationary vector time series and its application to models for a signal observed with noise. Annals of Statistics 7, 490–506.CrossRefGoogle Scholar
Dunsmuir, W. & Hannan, E.J. (1976) Vector linear time series models. Advances in Applied Probability 8, 339–364.CrossRefGoogle Scholar
Engle, R.F. & Granger, C.W.J. (1987) Cointegration and error correction: Representation, estimation, and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Gourieroux, C. & Monfort, A. (1980). Sufficient linear structures: Econometric applications. Econometrica 48, 1083–1097.CrossRefGoogle Scholar
Granger, C.W.J. & Lee, T.-H. (1990) Multicointegration. Advances in Econometrics 8, 71–84.Google Scholar
Haldrup, N. (1991) Multivariate Regression Models with I(2)-Variables. Mimeo, Institute of Economics, University of Aarhus.Google Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Application. New York: Academic Press.Google Scholar
Hasza, D.P. & Fuller, W.A. (1979) Estimation for autoregressive processes with unit roots. Annals of Statistics 7, 1106–1120.CrossRefGoogle Scholar
Hendry, D.F. (1987) Econometric methodology: A personal perspective. In Bewley, T. (ed.), Advances in Econometrics, vol. 2, pp. 29–48. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254.CrossRefGoogle Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.CrossRefGoogle Scholar
Johansen, S. (1992a). A representation of vector autoregressive processes integrated of order 2. Econometric Theory 8, 188–202.CrossRefGoogle Scholar
Johansen, S. (1992b). A Statistical Analysis of Cointegration for 1(2) Variables. Mimeo, University of Copenhagen.Google Scholar
Kashyap, A.K. & Wilcox, D.W. (1993) Production and inventory control at the General Motors Corporation during the 1920's and 193O's. American Economic Review 83, 383–401.Google Scholar
King, R.G., Plosser, C.I., Stock, J.H. & Watson, M.W. (1991) Stochastic trends and economic fluctuations. American Economic Review 81, 819–840.Google Scholar
Park, J.Y. (1992) Canonical cointegrating regressions. Econometrica 60, 119–143.CrossRefGoogle Scholar
Park, J.Y. & Ogaki, M. (1991) Seemingly Unrelated Canonical Cointegrating Regressions. Working paper 280, The Rochester Center for Economic Research.Google Scholar
Park, J.Y. & Phillips, P.C.B. (1988) Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4, 468–497.CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1989) Statistical inference in regressions with integrated processes: Part 2. Econometric Theory 5, 95–131.CrossRefGoogle Scholar
Phillips, P.C.B. (1988) Spectral regression for cointegrated time series. In Barnett, W.A., Powell, J. & Tauchen, G. (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, pp. 413–435. Cambridge: Cambridge University Press.Google Scholar
Phillips, P.C.B. (1991a) Optimal inference in cointegrated systems. Econometrica 59, 283–306.CrossRefGoogle Scholar
Phillips, P.C.B. (1991b) The Tail Behavior of Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models. Discussion paper 999, Cowles Foundation.Google Scholar
Phillips, P.C.B. & Hansen, B. (1990) Statistical inference in instrumental variables regression with 1(1) processes. Review of Economic Studies 57, 99–125.CrossRefGoogle Scholar
Phillips, P.C.B. & Loretan, M. (1991) Estimating long run economic equilibria. Review of Economic Studies 59, 407–436.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Saikkonen, P. (1991). Asymptotically efficient estimation of cointegrating regressions. Econometric Theory 7, 1–21.CrossRefGoogle Scholar
Saikkonen, P. (1993). Estimation of cointegration vectors with linear restrictions. Econometric Theory 9, 19–35.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (1993) A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61, 783–820.CrossRefGoogle Scholar
Sweeting, T. (1983) On estimator efficiency in stochastic processes. Stochastic Processes and Their Applications 15, 93–98.CrossRefGoogle Scholar
Tanaka, K. (1992) Statistical Analysis of Higher Order Integrated and Cointegrated Processes. Mimeo, Hitotsubashi University.Google Scholar
Yoo, B.S. (1986) Multi–Cointegrated Time Series and Generalized Error-Correction Models. USCD discussion paper.Google Scholar