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Asymptotically Efficient Estimation of Cointegration Regressions

Published online by Cambridge University Press:  11 February 2009

Pentti Saikkonen
Affiliation:
University of Helsinki

Abstract

An asymptotic optimality theory for the estimation of cointegration regressions is developed in this paper. The theory applies to a reasonably wide class of estimators without making any specific assumptions about the probability distribution or short-run dynamics of the data-generating process. Due to the nonstandard nature of the estimation problem, the conventional minimum variance criterion does not provide a convenient measure of asymptotic efficiency. An alternative criterion, based on the concentration or peakedness of the limiting distribution of an estimator, is therefore adopted. The limiting distribution of estimators with maximum asymptotic efficiency is characterized in the paper and used to discuss the optimality of some known estimators. A new asymptotically efficient estimator is also introduced. This estimator is obtained from the ordinary least-squares estimator by a time domain correction which is nonparametric in the sense that no assumption of a finite parameter model is required. The estimator can be computed with least squares without any initial estimations.

Type
Articles
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

1.Anderson, T. W.The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proceedings of the American Mathematical Society 6 (1955): 170176.CrossRefGoogle Scholar
2.Basawa, I.V. & Scott, D.J.. Asymptotic Optimal Inference for Nonergodic Models. New York: Springer Verlag, 1983.CrossRefGoogle Scholar
3.Berk, K.N.Consistent autoregressive spectral estimates. The Annals of Statistics 2 (1974): 489502.CrossRefGoogle Scholar
4.Birnbaum, Z.W.On random variables with comparable peakedness. The Annals of Mathematical Statistics 19 (1948): 7681.CrossRefGoogle Scholar
5.Brillinger, D.R.Time Series: Data Analysis and Theory New York: Holt, Rinehart and Winston, 1975.Google Scholar
6.Engle, R.F. &Granger, C.W.J.. Cointegration and error correction: Representation, estimation and testing. Econometrica 55 (1987): 251276.CrossRefGoogle Scholar
7.Hannan, E.J.Multiple Time Series. New York: Wiley, 1970.CrossRefGoogle Scholar
8.Hannan, E.J. & Kavalieris, L.. Multivariate linear time series models. Advances in Applied Probability 16 (1984): 492561.CrossRefGoogle Scholar
9.Hansen, B.E. &Phillips, P.C.B.. Estimation and inference in models of cointegration: A simulation study. Advances in Econometrics, 1989: forthcoming.Google Scholar
10.Hendry, D.F. Econometric methodology: A personal perspective. In Bewley, T. (ed.), Advances in Econometrics Chapter 10 and pp. 2948. Cambridge: Cambridge University Press, 1987.CrossRefGoogle Scholar
11.Hendry, D.F.PC-GIVE: An Interactive Econometric Modelling System Version 6.01, 1987.Google Scholar
12.Jeganathan, P.An extension of a result of L. LeCam concerning asymptotic normality. Sankhya Series A 42 (1980): 146160.Google Scholar
13.Jeganathan, P.On the asymptotic theory of estimation when the limit of the log-likelihood ratios is mixed normal. Sankhya Series A 44 (1982): 173212.Google Scholar
14.Johansen, S.Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12 (1988): 231254.CrossRefGoogle Scholar
15.Johansen, S. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Preprint, University of Copenhagen, 1989.Google Scholar
16.Johansen, S. & Juselius, K.. Hypothesis testing for cointegration vectors with an application to the demand for money in Denmark and Finland. Preprint, University of Copenhagen, 1988.Google Scholar
17.Lewis, R. & Reinsel, G.C.. Prediction of multivariate time series by autoregressive model fitting. Journal of Multivariate Analysis 16 (1985): 393411.CrossRefGoogle Scholar
18.Olkin, I. & Tong, Y.L.. Peakedness in multivariate distributions. In Gupta, S.S. & Berger, J.O. (eds.). Statistical Decision Theory and Related Topics IV, Vol. 2, pp. 373383. New York: Springer Verlag, 1988.CrossRefGoogle Scholar
19.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part I. Econometric Theory 4 (1988): 468497.CrossRefGoogle Scholar
20.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part II. Econometric Theory 5 (1989): 95131.CrossRefGoogle Scholar
21.Phillips, P.C.B.Reflections on econometric methodology. Economic Record 64 (1988): 344359.CrossRefGoogle Scholar
22.Phillips, P.C.B. Spectral regression for cointegrated time series. Cowles Foundation Discussion Paper No. 872, 1988.Google Scholar
23.Phillips, P.C.B. Optimal inference in cointegrated systems. Cowles Foundation Discussion Paper No. 866 (revised), 1990.Google Scholar
24.Phillips, P.C.B. & S.N., . Multiple time series regression with integrated processes. Review of Economic Studies 53 (1986): 473496.CrossRefGoogle Scholar
25.Phillips, P.C.B. & Hansen, B.E.. Statistical inference in instrumental variables regression with 1(1) processes. Review of Economic Studies 57 (1990): 99125.CrossRefGoogle Scholar
26.Phillips, P.C.B. & Loretan, M.. Estimating long run economic equilibria. Cowles Foundation Discussion Paper No. 928, 1989.Google Scholar
27.Phillips, P.C.B. & Park, J.Y.. Asymptotic equivalence of OLS and GLS in regressions with integrated regressors. Journal of the American Statistical Association 83 (1988): 111115.CrossRefGoogle Scholar
28.Rao, C.R.Linear Statistical Inference and Its Applications. New York: Wiley, 1973.CrossRefGoogle Scholar
29.Said, S.E. & Dickey, D.A.. Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71 (1984): 599607.CrossRefGoogle Scholar
30.Sherman, S.A theorem on convex sets with applications. The Annals of Mathematical Statistics 26 (1955): 763767.CrossRefGoogle Scholar
31.Stock, J.H.Asymptotic properties of least squares estimators of cointegrating vectors. Econometrica 56 (1987): 10351056.CrossRefGoogle Scholar
32.Sweeting, T.On estimator efficiency in stochastic processes. Stochastic Processes and their Applications 15 (1983): 9398.CrossRefGoogle Scholar