Hostname: page-component-6766d58669-bkrcr Total loading time: 0 Render date: 2026-05-24T00:26:45.352Z Has data issue: false hasContentIssue false
  • English
  • Français

Infinite-Order Cointegrated Vector Autoregressive Processes

Published online by Cambridge University Press:  11 February 2009

Pentti Saikkonen  and
HELMUT Lütkepohl
Pentti Saikkonen
Affiliation:
University of Helsinki
HELMUT Lütkepohl
Affiliation:
Humboldt University
Get access Rights & Permissions [Opens in a new window]

Abstract

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the relationships between the variables; therefore, they are important for applied work. Tests for linear restrictions on the coefficients of both the ECM and the pure VAR representation are considered under the present assumptions. It is found that they have limiting x2 distributions. Tests are also derived under the assumption that the number of restrictions goes to infinity with the sample size.

Information

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 5 , December 1996 , pp. 814 - 844
Copyright
Copyright © Cambridge University Press 1996

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

Berk, K.N. (1974) Consistent autoregressive spectral estimates. Annals of Statistics 2, 489–502.CrossRefGoogle Scholar
Bhansali, R.J. (1978) Linear prediction by autoregressive model Fitting in the time domain. Annals of Statistics 6, 224–231.CrossRefGoogle Scholar
Boudjellaba, H., Dufour, J.-M., & Roy, R. (1992) Testing causality between two vectors in multivariate ARMA models. Journal of the American Statistical Association 87, 1082–1090.CrossRefGoogle Scholar
Brillinger, D.A. (1975) Time Series, Data Analysis and Theory. New York: Holt, Rinehart and Winston.Google Scholar
Choi, I. (1993) Asymptotic normality of the least-squares estimates for higher order autoregressive integrated processes with some applications. Econometric Theory 9, 263–282.CrossRefGoogle Scholar
Dolado, J.J & Lütkepohl, H. (1996) Making Wald tests work for cointegrated systems. Econometric Reviews, forthcoming.CrossRefGoogle Scholar
Faust, J. (1995) Near observational equivalence and theoretical size problems with unit root tests. Econometric Theory, forthcoming.CrossRefGoogle Scholar
Hannan, E.J. & Deistler, M. (1988) The Statistical Analysis of Linear Systems. New York: Wiley.Google Scholar
Hasza, D.P. & Fuller, W.A. (1982) Testing for nonstationary parameter specifications in seasonal time series models. Annals of Statistics 10, 1209–1216.CrossRefGoogle Scholar
Johansen, S. (1989) Likelihood Based Inference on Cointegration. Theory and Applications. Bologna: Centra Interuniversitario di Econometria.Google Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.CrossRefGoogle Scholar
Lewis, R. & Reinsel, G.C. (1985) Prediction of multivariate time series by autoregressive model fitting. Journal of Multivariate Analysis 16, 393–411.CrossRefGoogle Scholar
Lütkepohl, H. (1991) Introduction to Multiple Time Series Analysis. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Lütkepohl, H. & Poskitt, D.S. (1996) Testing for causation using infinite order vector autoregressive processes. Econometric Theory 12, 61–87.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. & Loretan, M. (1991) Estimating long-run economic equilibria. Review of Economic Studies 58, 407–436.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Said, S.E. & Dickey, D.A. (1984) Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71, 599–607.CrossRefGoogle Scholar
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegration regressions. Econometric Theory 1, 1–21.CrossRefGoogle Scholar
Saikkonen, P. (1992) Estimation and testing of cointegrated systems by an autoregressive approximation. Econometric Theory 8, 1–27.CrossRefGoogle Scholar
Saikkonen, P. (1995) Dependent versions of a central limit theorem for the squared length of a sample mean. Statistics and Probability Letters 22, 185–194.CrossRefGoogle Scholar
Sims, C.A., Stock, J.H., & Watson, M.W. (1990) Inference in linear time series models with some unit roots. Econometrica 58, 113–144.CrossRefGoogle Scholar
Toda, H.Y. & Phillips, P.C.B. (1993a) The spurious effect of unit roots on exogeneity tests in vector autoregressions: An analytical study. Journal of Econometrics 59, 229–255.CrossRefGoogle Scholar
Toda, H.Y. & Phillips, P.C.B. (1993b) Vector autoregression and causality. Econometrica 61, 1367–1393.CrossRefGoogle Scholar
Toda, H.Y. & Yamamoto, T. (1995) Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics 66, 225–250.CrossRefGoogle Scholar