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FURTHER RESULTS ON THE ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES

Published online by Cambridge University Press:  31 March 2005

Robert de Jong  and
Chien-Ho Wang
Robert de Jong
Affiliation:
Ohio State University
Chien-Ho Wang
Affiliation:
National Taipei University
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Abstract

This paper establishes various results involving functions of integrated processes. Two theorems—which improve similar results by Park and Phillips—are proved for averages of functions of an integrated process that has not been rescaled by the square root of sample size. In addition, two results are given that characterize asymptotic behavior of averages of nonintegrable functions of rescaled integrated processes; the observations close to the pole take over asymptotic behavior in that case. Throughout, we make the assumption that the innovations of the integrated process are a linear process.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 2 , April 2005 , pp. 413 - 430
Copyright
© 2005 Cambridge University Press

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References

REFERENCES

Chung, K.L. & R.J. Williams (1990) Introduction to Stochastic Integration, 2nd ed. Birkhäuser.
de Jong, R.M. (2004) Addendum to “Asymptotics for nonlinear transformations of integrated time series.” Econometric Theory (forthcoming).Google Scholar
Park, J.Y. & P.C.B. Phillips (1999) Asymptotics for nonlinear transformations of integrated time series. Econometric Theory 15, 269–298.Google Scholar
Pötscher, B.M. (2004) Nonlinear functions and convergence to Brownian motion: Beyond the continuous mapping theorem. Econometric Theory 20, 1–22.Google Scholar