Hostname: page-component-6898cfcb55-zkb6p Total loading time: 0 Render date: 2026-11-11T19:14:26.676Z Has data issue: false hasContentIssue false
  • English
  • Français

Limit Theory forM-Estimates in an IntegratedInfinite Variance

Published online by Cambridge University Press:  11 February 2009

Keith Knight
Get accessRights & Permissions [Opens in a new window]

Abstract

We consider the limiting distributions ofM-estimates of an“autoregressive” parameter when the observationscome from an integrated linear process with infinitevariance innovations. It is shown thatM-estimates are, asymptotically,infinitely more efficient than the least-squaresestimator (in the sense that they have a faster rateof convergence) and are conditionally asymptoticallynormal.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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 Unpublished manuscript, Boston University, 1989.Google Scholar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