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Principal Components Analysis of Cointegrated Time Series

Published online by Cambridge University Press:  11 February 2009

David Harris
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Abstract

This paper considers the analysis of cointegrated time series using principal components methods. These methods have the advantage of requiring neither the normalization imposed by the triangular error correction model nor the specification of a finite-order vector autoregression. An asymptotically efficient estimator of the cointegrating vectors is given, along with tests forcointegration and tests of certain linear restrictions on the cointegrating vectors. An illustrative application is provided.

Type
Research Article
Information
Econometric Theory , Volume 13 , Issue 4 , February 1997 , pp. 529 - 557
Copyright
Copyright © Cambridge University Press 1997

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References

REFERNCES

Ahn, S.K. & Reinsel, G.C. (1990) Estimation for partially nonstationary multivariate autorcgressive models. Journal of the American Statistical Association 85, 813–823.10.1080/01621459.1990.10474945CrossRefGoogle Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.10.2307/2938229CrossRefGoogle Scholar
Brillinger, D.R. (1981) Time Series: Data Analysis and Theory. New York: McGraw-Hill.Google Scholar
Choi, I. (1994) Residual-based tests for the null of stationarity with applications to U.S. macroeconomic time series. Econometric Theory 10, 720–746.10.1017/S0266466600008744CrossRefGoogle Scholar
Choi, I. & Ahn, B.C. (1995) Testing for cointegration in a system of equations. Econometric Theory 11, 952–983.10.1017/S0266466600009932CrossRefGoogle Scholar
Engle, R.F. & C.W.J. Granger (1987) Cointegration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.10.2307/1913236CrossRefGoogle Scholar
Engle, R.F. & Yoo, B.S. (1991) Cointegrated time series: An overview with new results. In Engle, R.F. & Granger, C.W.J. (eds.), Long Run Economic Relationships: Readings in Cointegration, pp. 237–266. Oxford: Oxford University Press.CrossRefGoogle Scholar
Gonzalo, J. (1994) Five alternative methods of estimating long-run equilibrium relationships. Journal of Econometrics 60, 203–233.10.1016/0304-4076(94)90044-2CrossRefGoogle Scholar
Hansen, B.E. (1992a) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489–500.10.1017/S0266466600013189CrossRefGoogle Scholar
Hansen, B.E. (1992b) Tests for parameter instability in regressions with 1(1) processes. Journal of Business and Economic Statistics 10, 321–335.Google Scholar
Harris, D. (1996) Principal Components Analysis of Cointegrated Tims Series. Working paper 2/96, Monash University.Google Scholar
Harris, D. & Inder, B. (1994) A test of the null hypothesis of cointegration. In Hargreaves, C. (ed)., Nonstationary Time Series Analysis and Cointegration, pp. 133–152. Oxford: Oxford University Press.CrossRefGoogle Scholar
Inder, B. (1995) Finite Sample Arguments for Appropriate Estimation of Cointegrating Relationships. Working paper, Monash University.Google Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254.Google Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.Google Scholar
Johansen, S. & Juselius, K. (1992) Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK. Journal of Econometrics 53, 211–244.10.1016/0304-4076(92)90086-7CrossRefGoogle Scholar
King, R.G., Plosser, C.I. Stock, J.H., & Watson, M.W. (1991) Stochastic trends and economic fluctuations. The American Economic Review 81, 819–840.Google Scholar
Kwiatkowski, D., P.C.B. Phillips, Schmidt, P., & Shin, Y. (1992) Testing the null 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, 159–178.10.1016/0304-4076(92)90104-YCrossRefGoogle Scholar
Park, J.Y. (1992) Canonical cointegrating regressions. Econometrica 60, 119–143.10.2307/2951679CrossRefGoogle Scholar
Park, J.Y & P.C.B. Phillips (1988) Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4, 468–498.10.1017/S0266466600013402CrossRefGoogle Scholar
Phillips, P.C.B. (1991a) Optimal inference in cointegrated systems. Econometrica 59, 283–306.Google Scholar
Phillips, P.C.B. (1991b) Spectral regression for cointegrated time series. In Barnett, W.A., Powell, J., & Tauchen, G.E. (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, pp. 413–435. Cambridge: Cambridge University Press.Google Scholar
Phillips, P.C.B. & Durlauf, S.N. (1986) Multiple time series regression with integrated processes. Review of Economic Studies 53, 473–495.Google Scholar
Phillips, P.C.B. & Hansen, B.E. (1990) Statistical inference in instrumental variables regression with 1(1) processes. Review of Economic Studies 57, 99–125.10.2307/2297545CrossRefGoogle Scholar
Phillips, P.C.B. & Loretan, M. (1991) Estimating long-run economic equilibria. Review of Economic Studies 58, 407–436.10.2307/2298004CrossRefGoogle Scholar
Phillips, P.C.B. & Ouiiaris, S. (1990) Asymptotic properties of residual-based tests for cointegration. Econometrica 58, 165–193.10.2307/2938339CrossRefGoogle Scholar
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21.10.1017/S0266466600004217CrossRefGoogle Scholar
Saikkonen, P. (1992) Estimation and testing of cointegrated systems by an autoregressive approximation. Econometric Theory 8, 1–27.10.1017/S0266466600010720CrossRefGoogle Scholar
Shin, Y. (1994) A residual-based test of the null of cointegration against the alternative of no cointegration. Econometric Theory 10, 91–115.10.1017/S0266466600008240CrossRefGoogle Scholar
Stock, J.H. (1987) Asymptotic properties of least squares estimators of cointegrating vectors. Econometrica 55, 1035–1056.10.2307/1911260CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (1988) Testing for common trends. Journal of the American Statistical Association 83, 1097–1107.10.1080/01621459.1988.10478707CrossRefGoogle Scholar
Stock, J.H. & (Watson, M.W. (1993) A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61, 783–820.Google Scholar
Yang, M. (1994) Canonical Correlation Analysis of Cointegrated Processes. Discussion paper 94/10, University of New South Wales, School of Economics.Google Scholar