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The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii

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  • Davidson, James
  • de Jong, Robert M.

Abstract

This paper derives a functional central limit theorem for the partial sums of fractionally integrated processes, otherwise known as I(d) processes for d 1/2. Such processes have long memory, and the limit distribution is the so-called fractional Brownian motion, having correlated increments even asymptotically. The underlying shock variables may themselves exhibit quite general weak dependence by being near-epoch-dependent functions of mixing processes. Several weak convergence results for stochastic integrals having fractional integrands and weakly dependent integrators are also obtained. Taken together, these results permit I(p + d) integrands for any integer p 1.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 16 (2000)
Issue (Month): 05 (October)
Pages: 643-666

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Handle: RePEc:cup:etheor:v:16:y:2000:i:05:p:643-666_16

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