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A SIEVE BOOTSTRAP TEST FOR COINTEGRATION INA CONDITIONAL ERROR CORRECTION MODEL

Published online by Cambridge University Press:  26 October 2009

Franz C. Palm ,
Stephan Smeekes  and
Jean-Pierre Urbain
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Abstract

In this paper we propose a bootstrap version of theWald test for cointegration in a single-equationconditional error correction model. The multivariatesieve bootstrap is used to deal with dependence inthe series. We show that the introduced bootstraptest is asymptotically valid. We also analyze thesmall sample properties of our test by simulationand compare it with the asymptotic test and severalalternative bootstrap tests. The bootstrap testoffers significant improvements in terms of sizeproperties over the asymptotic test, while havingsimilar power properties. The sensitivity of thebootstrap test to the allowance for deterministiccomponents is also investigated. Simulation resultsshow that the tests with sufficient deterministiccomponents included are insensitive to the truevalue of the trends in the model and retain correctsize.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 647 - 681
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

Previous versions of this paper have beenpresented at the Econometric Society EuropeanMeeting in Milan, August 2008; at theInternational Workshop on Recent Advances in TimeSeries Analysis in Cyprus, June 2008; at theWorkshop on Bootstrap and Time Series inKaiserslautern, June 2008; at the conferenceentitled Inference and Tests in Econometrics, ATribute to Russell Davidson in Marseille, April2008; at an Ente Luigi Einaudi Seminar inEconometrics in Rome, November 2007; and at thefirst workshop of the Methods in InternationalFinance Network in Maastricht, September 2007. Wegratefully acknowledge the comments byparticipants at these seminars and by AndersSwensen, Pentti Saikkonen, and three anonymousreferees. We thank NWO and the Royal NetherlandsAcademy of Arts and Sciences for financialsupport.

References

REFERENCES

Ahlgren, N.J.C. (2000) Bootstrapping the Error Correction Model Cointegration Test. Working paper 428, Swedish School of Economics and Business Administration.Google Scholar
Banerjee, A., Dolado, J.J., & Mestre, R. (1998) Error-correction mechanism tests for cointegration in a single-equation framework. Journal of Time Series Analysis 19, 267–283.CrossRefGoogle Scholar
Basawa, I.V., Mallik, A.K., McCormick, W.P., Reeves, J.H., & Taylor, R.L. (1991) Bootstrapping unstable first-order autoregressive processes. Annals of Statistics 19, 1098–1101.CrossRefGoogle Scholar
Berger, E. (1991) Majorization, exponential inequalities and almost sure behavior of vector-valued random variables. Annals of Probability 19, 1206–1226.CrossRefGoogle Scholar
Berk, K.N. (1974) Consistent autoregressive spectral estimates. Annals of Statistics 2, 489–502.CrossRefGoogle Scholar
Boswijk, H.P. (1994) Testing for an unstable root in conditional and structural error correction models. Journal of Econometrics 63, 37–60.10.1016/0304-4076(93)01560-9Google Scholar
Boswijk, H.P. & Franses, P.H. (1992) Dynamic specification and cointegration. Oxford Bulletin of Economics and Statistics 54, 369–381.CrossRefGoogle Scholar
Bühlmann, P. (1995) Moving-average representations of autoregressive approximations. Stochastic Processes and Their Applications 60, 331–342.CrossRefGoogle Scholar
Bühlmann, P. (1997) Sieve bootstrap for time series. Bernoulli 3, 123–148.Google Scholar
Chang, Y. & Park, J.Y. (2002) On the asymptotics of ADF tests for unit roots. Econometric Reviews 21, 431–447.Google Scholar
Chang, Y. & Park, J.Y. (2003) A sieve bootstrap for the test of a unit root. Journal of Time Series Analysis 24, 379–400.10.1111/1467-9892.00312CrossRefGoogle Scholar
Chang, Y., Park, J.Y., & Song, K. (2006) Bootstrapping cointegrating regressions. Journal of Econometrics 133, 703–739.Google Scholar
Einmahl, U. (1987) A useful estimate in the multidimensional invariance principle. Probability Theory and Related Fields 76, 81–101.10.1007/BF00390277Google Scholar
Engle, R.F. & Granger, C.W.J. (1987) Co-integration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.CrossRefGoogle Scholar
Hannan, E.J. & Kavalieris, L. (1986) Regression, autoregression models. Journal of Time Series Analysis 7, 27–49.CrossRefGoogle Scholar
Johansen, S. (1995) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.CrossRefGoogle Scholar
Johansen, S. & Juselius, K. (1990) Maximum likelihood estimation and inference on cointegration - with applications to the demand for money. Oxford Bulletin of Economics and Statistics 54, 169–210.Google Scholar
Kremers, J.J.M., Ericsson, N.R., & Dolado, J.J. (1992) The power of cointegration tests. Oxford Bulletin of Economics and Statistics 52, 325–348.Google Scholar
Mantalos, P. & Shukur, G. (1998) Size and power of the error correction model cointegration test. A bootstrap approach. Oxford Bulletin of Economics and Statistics 60, 249–255.10.1111/1468-0084.00097Google Scholar
Palm, F.C., Smeekes, S., & Urbain, J.-P. (2008) Bootstrap unit root tests: Comparison and extensions. Journal of Time Series Analysis 29, 371–401.Google Scholar
Paparoditis, E. (1996) Bootstrapping autoregressive and moving average parameter estimates of infinite order vector autoregressive processes. Journal of Multivariate Analysis 57, 277–296.Google Scholar
Paparoditis, E. & Politis, D.N. (2003) Residual-based block bootstrap for unit root testing. Econometrica 71, 813–855.Google Scholar
Paparoditis, E. & Politis, D.N. (2005) Bootstrapping unit root tests for autoregressive time series. Journal of the American Statistical Association 100, 545–553.Google Scholar
Park, J.Y. (2002) An invariance principle for sieve bootstrap in time series. Econometric Theory 18, 469–490.CrossRefGoogle Scholar
Park, J.Y. (2003) Bootstrap unit root tests. Econometrica 71, 1845–1895.Google Scholar
Park, J.Y. & Phillips, P.C.B. (1989) Statistical inference in regressions with integrated processes: Part 2. Econometric Theory 5, 95–131.Google Scholar
Pesavento, E. (2004) Analytical evaluation of the power of tests for the absence of cointegration. Journal of Econometrics 122, 349–384.Google Scholar
Phillips, P.C.B. (1988) Weak convergence to the matrix stochastic integral . Journal of Multivariate Analysis 24, 252–264.10.1016/0047-259X(88)90039-5CrossRefGoogle Scholar
Phillips, P.C.B. & Ouliaris, S. (1990) Asymptotic properties of residual based tests for cointegration. Econometrica 58, 165–193.10.2307/2938339CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.10.1214/aos/1176348666Google Scholar
Poskitt, D.S. (1994) A note on autoregressive modeling. Econometric Theory 10, 884–899.Google Scholar
Seo, M. (2006) Bootstrap testing for the null of no cointegration in a threshold vector error correction model. Journal of Econometrics 134, 129–150.10.1016/j.jeconom.2005.06.018CrossRefGoogle Scholar
Swensen, A.R. (2006) Bootstrap algorithms for testing and determining the cointegration rank in VAR models. Econometrica 74, 1699–1714.CrossRefGoogle Scholar
Trenkler, C. (2009) Bootstrapping systems cointegration tests with a prior adjustment for deterministic terms. Econometric Theory 25, 243–269.CrossRefGoogle Scholar
Van Giersbergen, N.P.A. & Kiviet, J.F. (1996) Bootstrapping a stable AD model: Weak vs strong exogeneity. Oxford Bulletin of Economics and Statistics 58, 631–656.CrossRefGoogle Scholar
Zivot, E. (2000) The power of single equation tests for cointegration when the cointegrating vector is prespecified. Econometric Theory 16, 407–439.CrossRefGoogle Scholar