Martingale Approximations for Sums of Stationary Processes

@inproceedings{Wu2003MartingaleAF,
  title={Martingale Approximations for Sums of Stationary Processes},
  author={Wei Biao Wu and Michael Woodroofe},
  year={2003}
}
Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first shown that a martingale approximation is necessary for such normality and then that the sums are asymptotically normal if and only if the approximating martingales satisfy a Lindeberg-Feller Condition. Using the explicit construction of the approximating… CONTINUE READING

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Showing 1-10 of 23 references

Central limit theorems for functionals of linear processes and their

  • W B.
  • shifts. Stoc. Proc. Appl.,
  • 2002
Highly Influential
6 Excerpts

Some limit theorems for stationary processes. Theory Probab

  • I. A. Ibragimov
  • 1962
Highly Influential
7 Excerpts

Independent and Stationary Sequences of Random Variables

  • I. A. IBRAGIMOV, YU. V. LINNIK
  • 1971
Highly Influential
2 Excerpts

Independent and stationary sequences

  • I. A. Ibragimov, Yu. V. Linnik
  • 1971
Highly Influential
2 Excerpts

Central limit theorems for functionals of linear processes and their applications

  • W. B. WU, M. WOODROOFE
  • Statist . Sinica
  • 2002

Necessary and sufficient conditions for the conditional central limit theorem

  • J. DEDECKER, P. MERLEVEDE
  • Ann . Probab .
  • 2002
1 Excerpt

A new weak dependence condition and applications to moment inequalities

  • P. Doukhan
  • Stoch . Proc . Appl .
  • 1999
1 Excerpt

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