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Limit Theory for M-Estimates in an Integrated Infinite Variance

Published online by Cambridge University Press:  11 February 2009

Keith Knight
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Abstract

We consider the limiting distributions of M-estimates of an “autoregressive” parameter when the observations come from an integrated linear process with infinite variance innovations. It is shown that M-estimates are, asymptotically, infinitely more efficient than the least-squares estimator (in the sense that they have a faster rate of convergence) and are conditionally asymptotically normal.

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 2 , June 1991 , pp. 200 - 212
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

1. Avram, F. & Taqqu, M.S.. Weak convergence of sums of moving averages in the a-stable domain of attraction. Unpublished manuscript, Boston University, 1989.Google Scholar
2. Beveridge, S. & Nelson, C.R.. A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the “business cycle”. Journal of Monetary Economics 7 (1981): 151–174.10.1016/0304-3932(81)90040-4CrossRefGoogle Scholar
3. Billingsley, P. Convergence of Probability Measures. New York: Wiley, 1968.Google Scholar
4. Billingsley, P. Weak Convergence of Measures: Applications in Probability. Philadelphia: SIAM, 1971.10.1137/1.9781611970623CrossRefGoogle Scholar
5. Chan, N.H. Inference for near integrated time series with infinite variance. Journal of the American Statistical Association 85 (1990): 1069–1074.10.1080/01621459.1990.10474977CrossRefGoogle Scholar
6. Chan, N.H. & Tran, L.T.. On the first order autoregressive process with infinite variance. Econometric Theory 5 (1989): 354–362.10.1017/S0266466600012561CrossRefGoogle Scholar
7. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. II (Second Edition). New York: Wiley, 1971.Google Scholar
8. Gordin, M.I. The central limit theorem for stationary processes. Soviet Mathematics Doklady 10 (1969): 1174–1176.Google Scholar
9. Hall, P. & Heyde, C.C.. Martingale Limit Theory and Its Application. New York: Academic Press, 1980.Google Scholar
10. Knight, K. Limit theory for autoregressive parameters in an infinite variance random walk. Canadian Journal of Statistics (1989): 261–278.10.2307/3315522CrossRefGoogle Scholar
11. Pham, T. & Tran, L.. Some mixing properties of time series models. Stochastic Processes and Their Applications 19 (1985): 297–303.10.1016/0304-4149(85)90031-6CrossRefGoogle Scholar
12. Phillips, P.C.B. Time series regression with a unit root and infinite-variance errors. Econometric Theory 6 (1990): 44–62.10.1017/S0266466600004904CrossRefGoogle Scholar
13. Pollard, D. Convergence of Stochastic Processes. New York: Springer-Verlag, 1984.10.1007/978-1-4612-5254-2CrossRefGoogle Scholar
14. Resnick, S. & Greenwood, P.. A bivariate stable characterization and domains of attraction. Journal of Multivariate Analysis 9 (1979): 206–221.10.1016/0047-259X(79)90079-4CrossRefGoogle Scholar