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Strong Laws for Dependent HeterogeneousProcesses

Published online by Cambridge University Press:  11 February 2009

Bruce E. Hansen
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Abstract

This paper presents maximal inequalities and strong lawof large numbers for weakly dependent heterogeneousrandom variables. Specifically considered areLr mixingales forr > 1, strong mixingsequences, and near epoch dependent (NED) sequences.We provide the first strong law forLr-boundedLr mixingales and NEDsequences for 1 > r > 2. The strong lawspresented for α-mixing sequences are lessrestrictive than the laws of McLeish [8].

Information

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 2 , June 1991 , pp. 213 - 221
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

1. Andrews, D.W.K. Consistency in nonlinear econometric models: a generic uniform law of large numbers. Econometrica 55 (1987): 1465–1471.10.2307/1913568CrossRefGoogle Scholar
2. Andrews, D.W.K. Laws of large numbers for dependent non-identically distributed random variables. Econometric Theory 4 (1988): 458–467.10.1017/S0266466600013396CrossRefGoogle Scholar
3.Billingsley, P. Convergence of Probability Measures. New York: Wiley, 1968.Google Scholar
4. Gallant, A.R. & White, H.. A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. New York: Basil Blackwell, 1988.Google Scholar
5. Granger, C.W.J. & Joyeux, R.. An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1 (1980): 15–29.10.1111/j.1467-9892.1980.tb00297.xCrossRefGoogle Scholar
6.Hall, P. & Heyde, C.C.. Martingale Limit Theory and Its Application. New York: Academic Press, 1980.Google Scholar
7. Ibragimov, I.A. Some limit theorems for stationary processes. Theory of Probability and Its Applications 7 (1962): 349–382.10.1137/1107036CrossRefGoogle Scholar
8. McLeish, D.L. A maximal inequality and dependent strong laws. The Annals of Probability 5 (1975): 829–839.Google Scholar
9. Phillips, P.C.B. & Solo, V.. Asymptotics for linear processes. Cowles Foundation Discussion Paper No. 932 (1989).Google Scholar
10 Potscher, B.M. & Prucha, I.R.. A uniform law of large numbers for dependent and heterogeneous data processes. Econometrica 57 (1989): 675–683.10.2307/1911058CrossRefGoogle Scholar
11. Sowell, F. The fractional unit root distribution. Econometrica 58 (1990): 495–505.10.2307/2938213CrossRefGoogle Scholar
12. Wooldridge, J.M. & White, H.. Some invariance principles and central limit theorems for dependent heterogeneous processes. Econometric Theory 4 (1988): 210–230.10.1017/S0266466600012032CrossRefGoogle Scholar