Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T22:16:08.107Z Has data issue: false hasContentIssue false
  • English
  • Français

A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration

Published online by Cambridge University Press:  11 February 2009

Yongcheol Shin
Yongcheol Shin
Affiliation:
University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a residual-based test of the null of cointegration using a structural single equation model. It is shown that the limiting distribution of the test statistic for cointegration can be made free of nuisance parameters when the cointegrating relation is efficiently estimated. The limiting distributions are given in terms of a mixture of a Brownian bridge and vector Brownian motion. It is also shown that this test is consistent. Critical values are given for standard, demeaned, and detrended cases. Combining results from our test for cointegration with results from the Phillips-Ouliaris test for no cointegration, we find that there is evidence of cointegration between real consumption and real disposable income over the postwar period.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 1 , March 1994 , pp. 91 - 115
Copyright
Copyright © Cambridge University Press 1994

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

1.Andrews, D.W.K.Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59 (1991): 817–858.CrossRefGoogle Scholar
2.Andrews, D.W.K. & Monahan, J.C.. An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60 (1992): 953–966.Google Scholar
3.Berk, K.N.Consistent autoregressive spectral estimates. Annals of Statistics 21 (1974): 489–502.Google Scholar
4.Campbell, J.Y. & Perron, P.. Pitfalls and opportunities: What macroeconomists should know about unit roots. Unpublished manuscript prepared for NBER Macroeconomic Conference, 1991.CrossRefGoogle Scholar
5.Engle, R.F. & Granger, C.W.J.. Cointegration and error correction representation: Estimation and testing. Econometrica 55 (1987): 251–276.CrossRefGoogle Scholar
6.Granger, C.W.J. & Lee, T.-H.. Multicointegration. Advances in Econometrics 8 (1990): 71–84.Google Scholar
7.Hansen, B.Tests for parameter instability in regressions with 1(1) processes. Journal of Business and Economic Statistics 10 (1992): 321–335.Google Scholar
8.Hansen, B.Consistent covariance matrix estimation for dependent heterogeneous processes. Econometrica 60 (1992): 967–972.CrossRefGoogle Scholar
9.Hansen, B.Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8 (1992): 489–500.CrossRefGoogle Scholar
10.Johansen, S.Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59 (1991): 1551–1580.Google Scholar
11.Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. & Shin, Y.. Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics 54 (1992): 159–178.Google Scholar
12.Kwiatkowski, D., Phillips, P.C.B. & Schmidt, P.. Testing for stationarity in the components representation of a time series. Econometric Theory 8 (1992): 586–591.CrossRefGoogle Scholar
13.Newey, W.K. & West, K.D.. A simple, positive semidefinite, heteroskedasticity and autocorrelated consistent covariance matrix. Econometrica 55 (1987): 703–708.CrossRefGoogle Scholar
14.Nyblom, J.Testing for the constancy of parameters over time. Journal of American Statistical Association 84 (1989): 223–230.CrossRefGoogle Scholar
15.Ogaki, M. & Park, J.Y.. A cointegration approach to estimating preference parameters. Rochester Center for Economic Research Working Paper No. 209, University of Rochester, 1989.Google Scholar
16.Park, J.Y. Testing for unit roots by variable addition. In Fomby, T.B. and Rhodes, G.F. (eds.), Advances in Econometrics: Cointegration, Spurious Regressions, and Unit Roots. Greenwich: JAI Press, 1990.Google Scholar
17.Park, J.Y.Canonical cointegrating regressions. Econometrica 60 (1992): 119–143.CrossRefGoogle Scholar
18.Park, J.Y., Ouliaris, S. & Choi, B.. A new approach to testing for a unit root. Unpublished manuscript. Cornell University, 1988.Google Scholar
19.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4 (1988): 468–498.Google Scholar
20.Phillips, P.C.B.Understanding spurious regressions in econometrics. Journal of Econometrics 33 (1986): 311–340.CrossRefGoogle Scholar
21.Phillips, P.C.B.Weak convergence of sample covariance matrices to stochastic integrals via martingale approximations. Econometric Theory 4 (1988): 528–533.CrossRefGoogle Scholar
22.Phillips, P.C.B.Optimal inference in cointegrated systems. Econometrica 59 (1991): 283–306.CrossRefGoogle Scholar
23.Phillips, P.C.B. Spectral regression for cointegrated time series. In Barnett, W. (ed.), Nonparametric and Semiparametric Methods in Economics and Statistics. New York: Cambridge University Press, 1991.Google Scholar
24.Phillips, P.C.B. & Durlauf, S.N.. Multiple time series regression with integrated processes. Review of Economic Studies 53 (1986): 473–496.Google Scholar
25.Phillips, P.C.B. & Hansen, B.. Statistical inference in instrumental variables regression with 1(1) processes. Review of Economic Studies 57 (1990): 99–125.CrossRefGoogle Scholar
26.Phillips, P.C.B. & Loretan, M.. Estimating long run economic equilibria. Review of Economic Studies 58 (1991): 407–436.Google Scholar
27.Phillips, P.C.B. & Ouliaris, S.. Asymptotic properties of residual based tests for cointegration. Econometrica 58 (1990): 165–193.CrossRefGoogle Scholar
28.Phillips, P.C.B. & Perron, P.. Testing for a unit root in time series regression. Biometrika 75 (1988): 335–346.CrossRefGoogle Scholar
29.Phillips, P.C.B. & Ploberger, W.. Posterior odds testing for a unit root with data-based model selection. Cowles Foundation Discussion Paper No. 1017, Yale University, 1992.Google Scholar
30.Press, W.H., Flannery, B.P., Teukolsky, S.A. & Vetterling, W.T.. Numerical Recipes: The Art of Statistical Computing. New York: Cambridge University Press, 1986.Google Scholar
31.Quintos, C.E. & Phillips, P.C.B.. Parameter constancy in cointegrating regressions. Unpublished manuscript. Yale University, 1992.Google Scholar
32.Said, S.E. & Dickey, D.A.. Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71 (1984): 599–607.CrossRefGoogle Scholar
33.Saikkonen, P.Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7 (1991): 1–21.Google Scholar
34.Stock, J.H. & Watson, M.W.. Testing for common trends. Journal of American Statistical Association 83 (1988): 1097–1107.Google Scholar
35.Stock, J.H. & Watson, M.W.. A simple estimator of cointegrating vectors in higher order integrated systems. Forthcoming in Econometrica.Google Scholar
36.Tanaka, K.An alternative approach to the asymptotic theory of spurious regression, cointegration, and near cointegration. Econometric Theory 9 (1993): 36–61.CrossRefGoogle Scholar
37.Wooldridge, J. Notes on regressions with difference stationary data. Unpublished manuscript, Massachusetts Institute of Technology, 1991.Google Scholar