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ESTIMATION OF COINTEGRATING VECTORS WITH TIME SERIES MEASURED AT DIFFERENT PERIODICITY

Published online by Cambridge University Press:  19 July 2005

Gabriel Pons  and
Andreu Sansó
Gabriel Pons
Affiliation:
University of Aarhus
Andreu Sansó
Affiliation:
University of the Balearic Islands
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Abstract

We discuss the effects of temporal aggregation on the estimation of cointegrating vectors and on testing linear restrictions on this vector. We adopt a discrete time approach and demonstrate, in contrast with the findings of Chambers (2003, Econometric Theory 19, 49–77), who adopts a continuous time approach, that in some situations, when the regressand must be aggregated, systematic sampling is preferable to average sampling for estimation purposes. Like Chambers, we show that the best aggregation scheme for regressors, in terms of asymptotic estimation efficiency, is always average sampling. We also show that different types of aggregation have no influence on the relative size of tests of linear restrictions on the cointegration vector.We thank Soren Johansen, Niels Haldrup, Raquel Waters, the associate editor, and two anonymous referees for their helpful comments. Of course, any remaining error is the responsibility of the authors. The first author gratefully acknowledges the financial support of a Marie Curie Fellowship of the European Community Programme “Improving the Human Research Potential and the Socio-Economic Knowledge Base” under contract HPMF-CT-2002-01662 and the Danish Research Council. The second author gratefully acknowledges the financial support of the Spanish Ministry of Science and Technology SEC2002-01512.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 4 , August 2005 , pp. 735 - 756
Copyright
© 2005 Cambridge University Press

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References

REFERENCES

Chambers, M.J. (2003) The asymptotic efficiency of cointegration estimators under temporal aggregation. Econometric Theory 19, 49–77.Google Scholar
Comte, F. (1999) Discrete and continuous time cointegration. Journal of Econometrics 88, 207–226.Google Scholar
Ericsson, N.R., D. Hendry, & H.-A. Tran (1994) Cointegration, seasonality, encompassing, and the demand for money in the UK. In C. Hargreaves (ed.), Nonstationary Time Series Analysis, pp. 179–224. Oxford University Press.
Gonzalo, J. (1994) Five alternative methods of estimating long-run equilibrium relationships. Journal of Econometrics 60, 203–233.Google Scholar
Granger, C.W.J. (1990) Aggregation of time-series variables: A survey. In T. Barker and M.H. Pesaran (eds.), Disaggregation in Econometric Modelling, pp. 17–34. Routledge.
Granger, C.W.J. & P.L. Siklos (1995) Systematic sampling, temporal aggregation, seasonal adjustment, and cointegration: Theory and evidence. Journal of Econometrics 66, 357–369.Google Scholar
Haldrup, N. (1994) The asymptotics of single-equation cointegration regressions with I(1) and I(2) variables. Journal of Econometrics 63, 153–181.Google Scholar
Hargreaves, C. (1994) A review of methods of estimating cointegrating relationships. In C. Hargreaves (ed.), Nonstationary Time Series Analysis, pp. 87–131. Oxford University Press.
Johansen, S. (1991) Estimation and hypothesis testing of cointegrating vectors in gaussian vector autoregressive models. Econometrica 59, 1551–1580.Google Scholar
Johansen, S. (1994) Estimating systems of trending variables. Econometric Reviews 13, 351–386.Google Scholar
Johansen, S. (1995) The role of ancillarity in inference for non-stationary variables. Economic Journal 13, 302–320.Google Scholar
Johansen, S. (2002) A small sample correction for tests of hypothesis on the cointegrating vectors. Journal of Econometrics 111, 195–221.Google Scholar
Johansen, S. & K. Juselius (1992) Testing structural hypothesis in a multivariate cointegration analysis of the PPP and UIP for UK. Journal of Econometrics 53, 211–244.Google Scholar
Jordà, O. (1999) Random-time aggregation in partial adjustment models. Journal of Business & Economic Statistics 17, 382–395.Google Scholar
Kitamura, Y. (1995) Estimation of cointegrated systems with I(2) processes. Econometric Theory 11, 1–24.Google Scholar
Marcellino, M. (1999) Some consequences of temporal aggregation in empirical analysis. Journal of Business & Economic Statistics 17, 129–136.Google Scholar
Niemi, H. (1984) The invertibility of sampled and aggregated ARMA models. Metrika 31, 43–50.Google Scholar
Park, J.Y. (1992) Canonical cointegrating regressions. Econometrica 60, 119–143.Google Scholar
Pesaran, M.H. & Y. Shin (1996) Cointegration and speed of convergence to equilibrium. Journal of Econometrics 71, 117–143.Google Scholar
Phillips, P.C.B. (1991a) Error correction and long-run equilibrium in continuous time. Econometrica 59, 967–980.Google Scholar
Phillips, P.C.B. (1991b) Optimal inference in cointegrated systems. Econometrica 59, 282–306.Google Scholar
Phillips, P.C.B. (1991c) Spectral regression for cointegrated time series. In W.A. Barnett, J. Powell, & G.E. Tauchen (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, pp. 413–436. Cambridge University Press.
Phillips, P.C.B. & B.E. Hansen (1990) Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99–125.Google Scholar
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegrating regressions. Econometric Theory 7, 1–21.Google Scholar
Stock, J.H. & M.W. Watson (1993) A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61, 783–820.Google Scholar
Stram, D.O. & W.W.S. Wei (1986) Temporal aggregation in the ARIMA process. Journal of Time Series Analysis 7, 279–292.Google Scholar
Telser, L.G. (1967) Discrete samples and moving sums in stationary stochastic processes. Journal of the American Statistical Association 62, 484–499.Google Scholar
Wei, W.S.W. (1989) Time Series Analysis: Univariate and Multivariate Methods. Addison-Wesley.