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CONVERGENCE OF INTEGRAL FUNCTIONALS OF STOCHASTIC PROCESSES

Published online by Cambridge University Press:  09 February 2006

István Berkes  and
Lajos Horváth
István Berkes
Affiliation:
Graz University of Technology
Lajos Horváth
Affiliation:
University of Utah
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Abstract

We investigate the convergence in distribution of integrals of stochastic processes satisfying a functional limit theorem. We allow a large class of continuous Gaussian processes in the limit. Depending on the continuity properties of the underlying process, local Lebesgue or Riemann integrability is required.We are grateful to the referees and Benedikt Pötscher for their helpful and constructive comments. The research of the first author was partially supported by OTKA grants T37668 and T43037 and NSF-OTKA grant INT-0223262. The research of the second author was partially supported by NATO grant PST.EAP.CLG 980599 and NSF-OTKA grant INT-0223262.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 2 , April 2006 , pp. 304 - 322
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Bingham, N.H., C.M. Goldie, & J.L. Teugels (1987) Regular Variation. Cambridge University Press.
Brockwell, P.J. & R.A. Davis (1991) Time Series: Theory and Methods, 2nd ed. Springer-Verlag.
Davydov, Yu. (1970) The invariance principle for stationary processes. Theory of Probability and Its Applications 15, 487–498.CrossRefGoogle Scholar
De Jong, R. (2004) Addendum to “Asymptotics for nonlinear transformation of integrated time series.” Econometric Theory 20, 623–635.Google Scholar
De Jong, R. & C. Wang (2005) Further results on the asymptotics for nonlinear transformation of integrated time series. Econometric Theory 21, 413–430.Google Scholar
Geman, D. & J. Horowitz (1980) Occupation densities. Annals of Probability 8, 1–67.CrossRefGoogle Scholar
Halmos, P. (1950) Measure Theory. Van Nostrand.
Hewitt, E. & K. Stromberg (1969) Real and Abstract Analysis. Springer-Verlag.
Horváth, L. & P. Kokoszka (1997) The effect of long-range dependence on change-point estimators. Journal of Statistical Planning and Inference 64, 57–81.CrossRefGoogle Scholar
Jeganathan, P. (2004) Convergence of functionals of sums of r.v.s to local times of fractional stable motions. Annals of Probability 32, 1771–1795.Google Scholar
Karatzas, I. & S.E. Shreve (1991) Brownian Motion and Stochastic Calculus, 2nd ed. Springer-Verlag.
Lukács, E. (1970) Characteristic Functions, 2nd ed. Griffin.
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.CrossRefGoogle Scholar
Riesz, F. & B. Szőkefalvi-Nagy (1990) Functional Analysis. Dover.
Shorack, G.R. & J.A. Wellner (1986) Empirical Processes with Applications to Statistics. Wiley.
Taqqu, M.S. (1975) Weak convergence to fractional Brownian motion and to the Rosenblatt process. Zietschrift für Wahrscheinlichskeitstheorie und Verwandte Gebiete 31, 287–302.CrossRefGoogle Scholar