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Convergence to Stochastic Integrals for Dependent Heterogeneous Processes

Published online by Cambridge University Press:  18 October 2010

Bruce E. Hansen
Bruce E. Hansen
Affiliation:
University of Rochester
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Abstract

This paper provides conditions to establish the weak convergence of stochastic integrals. The theorems are proved under the assumption that the innovations are strong mixing with uniformly bounded 2-h moments. Several applications of the results are given, relevant for the theories of estimation with I(1) processes, I(2) processes, processes with nonstationary variances, near-integrated processes, and continuous time approximations.

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Type
Articles
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Econometric Theory , Volume 8 , Issue 4 , December 1992 , pp. 489 - 500
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

1.Andrews, D. W. K.Laws of large numbers for dependent non-identically distributed random variables. Econometric Theory 4 (1988): 458–467.CrossRefGoogle Scholar
2.Billingsley, P.Convergence of Probability Measures. New York: Wiley, 1968.Google Scholar
3.Chan, N.H. & Wei, C.Z.. Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15 (1987): 1050–1063.Google Scholar
4.Chan, N.H. & Wei, C.Z.. Limiting distributions of least-squares estimates of unstable autoregressive processes. Annals of Statistics 16 (1988): 367–401.Google Scholar
5.Hall, P. & Heyde, C.C.. Martingale Limit Theory and Its Application. New York: Academic Press, 1980.Google Scholar
6.Hansen, B.E.Heteroskedastic cointegration. Journal of Econometrics (1992), forthcoming.Google Scholar
7.Hansen, B.E. Regression theory when variances are nonstationary. Unpublished manuscript, University of Rochester, 1990.Google Scholar
8.Hansen, B.E.Tests for parameter instability in regressions with 1(1) processes. Journal of Business and Economic Statistics 10 (1992): 321–335.Google Scholar
9.Jeganathan, P.On the asymptotic behavior of least-squares estimators in AR time series models with roots near the unit circle. Econometric Theory 1 (1991): 269–306.Google Scholar
10.Kurtz, T.G. & Protter, P.. Weak limit theorems for stochastic integrals and stochastic differential equations. The Annals of Probability 19 (1991): 1035–1070.CrossRefGoogle Scholar
11.McLeish, D.L.A maximal inequality and dependent strong laws. The Annals of Probability 3 (1975): 829–839.Google Scholar
12.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4 (1988): 468–497.CrossRefGoogle Scholar
13.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part 2. Econometric Theory 5 (1989): 95–131.CrossRefGoogle Scholar
14.Perron, P.A continuous time approximation to the first-order autoregressive process: The case without an intercept. Econometrica 59 (1991): 211–236.Google Scholar
15.Perron, P.A continuous time approximation to the stationary first-order autoregressive model. Econometric Theory 59 (1991): 236–252.CrossRefGoogle Scholar
16.Phillips, P.C.B.Time series regression with a unit root. Econometrica 55 (1987): 277–301.Google Scholar
17.Phillips, P.C.B.Towards a unified asymptotic theory for autoregression. Biometrika 74 (1987): 535–547.Google Scholar
18.Phillips, P.C.B.Weak convergence to the matrix stochastic integral 10BdB'. Journal of Multivariate Analysis 24 (1988): 252–264.Google Scholar
19.Phillips, P.C.B.Weak convergence of sample covariance matrices to stochastic integrals via martingale approximations. Econometric Theory 4 (1988): 528–533.Google Scholar
20.Phillips, P.C.B.Regression theory for near-integrated time series. Econometrica 56 (1988): 1021–1044.CrossRefGoogle Scholar
21.Protter, P.Stochastic Integration and Differential Equations: A New Approach. New York: Springer-Verlag, 1990.CrossRefGoogle Scholar
22.Strasser, H.Martingale difference arrays and stochastic integrals. Probability Theory and Related Fields 72 (1986): 83–98.CrossRefGoogle Scholar
23.Wooldridge, J.M. & White, H.. Some invariance principles and central limit theorems for dependent heterogeneous processes. Econometric Theory 4 (1988): 210–230.CrossRefGoogle Scholar